GIFT  or 

Daughter  of 

m  Stuart  Smith 


N 


PRACTICAL  CALCULATION 

OF 

DYNAMO-ELECIRIC 
MACHINES      ^ 


A    MANUAL 
FOR   ELECTRICAL   AND    MECHANICAL  ENGINEERS 

AND   A   TEXT-BOOK 
FOR   STUDENTS    OF    ELECTRO-TECHNICS 


BY 

ALFRED  E.  WIENER,  E.  E.,  M.  E. 

M.  A,  I.  E.  E. 


NEW  YORK 

THE   W.    J.    JOHNSTON   COMPANY 

253  BROADWAY 

1898 


COPYRIGHT,  1897,  BY 
THE  W.  J.  JOHNSTON  COMPANY 


PREFACE. 


IN  the  following  volume  an  entirely  practical  treatise  on 
dynamo-calculation  is  developed,  differing  from  the  usual 
text-book  methods,  in  which  the  application  of  the  various 
formulae  given  requires  more  or  less  experience  in  dynamo- 
design.  The  present  treatment  of  the  subject  is  based  upon 
results  obtained  in  practice  and  therefore,  contrary  to  the 
theoretical  methods,  gives  such  practical  experience.  Informa- 
tion of  this  kind  is  presented  in  the  form  of  more  than 
a  hundred  original  tables  and  of  nearly  five  hundred  formulae 
derived  from  the  data  and  tests  of  over  two  hundred  of  the 
best  modern  dynamos  of  American  as  well  as  European  make, 
comprising  all  the  usual  types  of  field  magnets  and  of  arma- 
tures, and  ranging  in  all  existing  sizes. 

The  author's  collection  of  dynamo-data  made  use  of  for  this 
purpose  contains  full  particulars  of  the  following  types  of  con- 
tinuous current  machines: 

American  Machines. 

Edison  Single  Horseshoe  Type,      .         .  .20  sizes. 

"        Iron-clad  Type,  .         .         .  .      10  " 

"        Multipolar  Central  Station  Type,  .      10  " 

11       Bipolar  Arc  Light  Type,     .         .  6  " 

"        Fourpolar  Marine  Type,      .         .  4  " 

"        Small  Low-Speed  Motor  Type,   .  4  " 

"        Railway  Motor  Type,          .         .  3  " 

Thomson-Houston  Arc  Light  Type,        .  .       9  " 

"  "  Spherical  Incandescent  Type,       4  " 

"  "         Multipolar  Type,       .  3  " 

"  "         Railway  Motor  Type,  .       2  " 

General  Electric  Radial  Outerpole  Type,  .      12  " 

Westinghouse  Engine  Type  ("Kodak ")  .     12  " 

Belt  Type,        .         .         .  8  " 

"  Arc  Light  Type,       .         .  .       3  " 

Brush  Double  Horseshoe  ("Victoria")  Type,     16  " 

iii 


IV  PREFACE. 

Sprague  Double  Magnet  Type,        .         .  13  sizes. 

Crocker-Wheeler  Bipolar  Motor  Type,   .  6  " 

"              "         Multipolar  Generator  Type,  2  " 

Entz  Multipolar  Marine  Type,                  .  5  " 

Weston  Double  Horseshoe  Type,   .         .  3  " 

Lundell  Multipolar  Type,        .  '       .         .  .       3  " 

Short  Multipolar  Railway  Motor  Type,  .       2  " 

Walker  Multipolar  Type,        .         .         .  .       a  " 

162 

English  Machines. 

Kapp  Inverted  Horseshoe  Type,    ...  4  sizes. 

Edison-Hopkinson  Single  Horseshoe  Type,  .       3  " 

Patterson  &  Cooper  "Phoenix"  Type,  .  .3  " 

Mather  &  Platt  "  Manchester  "  Type,    .  3  " 

Paris  &  Scott  Double  Horseshoe  Type,  .       2  " 

Crompton  Double  Horseshoe  Type,        .  .  size. 
Kennedy  Single  Magnet  Type, 
"  Leeds  "  Single  Magnet  Type,      . 
Immisch  Double  Magnet  Type,      . 
"Silvertown"  Single  Horseshoe  Type, 
Elwell-Parker  Single  Horseshoe  Type,  . 
Sayers  Double  Magnet  Type,          .         . 

22 

German  Machines. 

Siemens  &  Halske  Innerpole  Type,         .  .       3  sizes. 

"              "          Single  Horseshoe  Type,  .       2  " 

Allgemeine   E.  G. ,  Innerpole  Type,        .   .  *       3  " 

"              "       Outerpole  Type,      .  ••  '     3  " 

Schuckert  Multipolar  Flat  Ring  Type,    .  .       3  " 

Lahmeyer  Iron-clad  Type,      .         ..        .  ,       3  "  ' 

Naglo  Bros.  Innerpole  Type,        ,  .         .  .       2  " 

Fein  Innerpole  Type,      .         .        ^         ..  .       2  " 

41     Iron-clad  Type,       .       -.         .      '  .  .  '    2  " 

"     Inward  Pole  Horseshoe  Type,       :.  .       2  '* 

Guelcher  Multipolar  Type,     .     t  .         .  .       2  " 

Schorch  Inward  Pole  Type,    .         .         .  i  size. 

Kummer  &  Co.  Radial  Multipolar  Type,  .        i  «* 

Bollmann  Multipolar  Disc  Type,    .         .  i  " 

30 


PREFACE. 

French  Machines. 

Gramme  Bipolar  Type, 

Marcel  Deprez  Multipolar  Type,    .         . 
Desrozier  Multipolar  Disc  Type, 
Alsacian  Electric  Construction  Co.  Innerpole 
Type,        .         .         .         .         .         .         . 


Swiss  Machines. 

Oerlikon  Multipolar  Type,      ....  4  sizes. 

Bipolar  Iron-clad  Type,    .         .         .  2      " 

"         Bipolar  Double  Magnet  Type,          .  2     " 
Brown  Double  Magnet  Type  (Brown,  Boveri 

&  Co.),     .  .         .         .         .'    .    .  2     " 

Thury  Multipolar  Type,          .         .         .         .  i  size. 
Alioth     &     Co.     Radial      Outerpole     Type 

("Helvetia"),          V     '  .         .         .  i     " 


In  this  list  are  contained  the  generators  used  in  the  central 
stations  of  New  York,  Brooklyn,  Boston,  Chicago,  St.  Louis, 
and  San  Francisco,  United  States;  of  Berlin,  Hamburg,  Han- 
over, Duesseldorf,  and  Darmstadt,  Germany;  of  London, 
England;  of  Paris,  France;  and  others;  also  the  General 
Electric  Company's  large  power  generator  for  the  Intra- 
mural Railway  plant  at  the  Chicago  World's  Fair,  and  other 
dynamos  of  fame. 

The  author  believes  that  the  abundance  and  variety  of  his 
working  material  entitles  him  to  consider  his  formulae  and 
tables  as  universally  applicable  to  the  calculation  of  any 
dynamo. 

Although  being  intended  as  a  text-book  for  students  and 
a  manual  for  practical  dynamo-designers,  anyone  possessing 
a  but  fundamental  knowledge  of  arithmetic  and  algebra  will 
by  means  of  this  work  be  able  to  successfully  calculate  and 
design  any  kind  of  a  continuous-current  dynamo,  the  matter 
being  so  arranged  that  all  the  required  practical  information 
is  given  wherever  it  is.  needed  for  a  formula. 

The  treatise  as  here  presented  has  originated  from  notes 
prepared  by  the  author  for  the  purpose  of  instructing  his 


VI  PREFACE. 

classes  of  practical  workers  in  the  electrical  field,  and  upon  the 
success  experienced  with  these  it  was  decided  to  publish  the 
method  for  the  benefit  of  others. 

Since  the  book  is  to  be  used  for  actual  workshop  practice, 
the  formulae  are  so  prepared  that  the  results  are  obtained  in 
inches,  feet,  pounds,  etc.  But  since  the  time  is  approaching 
when  the  metric  system  will  be  universally  employed,  and  as 
the  book  is  written  for  the  future  as  well  as  for  the  present, 
the  tables  are  given  both  for  the  English  and  metric  systems 
of  measurement. 

As  far  as  the  principles  of  dynamo-electric  machinery  are 
concerned,  the  time-honored  method  of  filling  one-third  to 
one-half  of  each  and  every  treatise  on  dynamo  design  with 
chapters  on  magnetism,  electro-magnetic  induction,  etc.,  has 
in  the  present  volume  been  departed  from,  the  subject  of  it 
being  the  calculation  and  not  the  theory  of  the  dynamo.  For 
the  latter  the  reader  is  referred  to  the  numerous  text-books, 
notably  those  of  Professor  Silvanus  P.  Thompson,  Houston 
and  Kennelly,  Professor  D.  C.  Jackson,  Carl  Hering,  and 
Professor  Dr.  E.  Kittler.  Descriptions  of  executed  machines 
have  also  been  omitted  from  this  volume,  a  fairly  com- 
plete list  of  references  being  given  instead,  in  Chapter 
XIV. 

The  arrangement  of  the  Parts  and  Chapters  has  been  care- 
fully worked  out  with  regard  to  the  natural  sequence  of  the 
subject,  the  process  of  dynamo-calculation,  in  general,  con- 
sisting (i)  in  the  calculation  of  the  length  and  size  of  con- 
ductor required  for  a  given  output  at  a  certain  speed;  (2)  in 
the  arrangement  of  this  conductor  upon  a  suitable  armature; 
(3)  in  supplying  a  magnet  frame  of  proper  cross-section  to 
carry  the  magnetic  flux  required  by  that  armature,  and  (4)  in 
determining  the  field  winding  necessary  to  excite  the  magnet- 
izing force  required  to  produce  the  desired  flux. 

Numerous  complete  examples  of  practical  dynamo  calcula- 
tion are  given  in  Part  VIII.,  the  single  cases  being  chosen 
with  a  view  of  obtaining  the  greatest  possible  variety  of  dif- 
ferent designs  and  varying  conditions.  The  leakage  examples 
in  Chapter  XXX.  not  only  demonstrate  the  practical  applica- 
tion of  the  formulae  given  in  Chapters  XII.  and  XIII.,  but 
also  show  the  accuracy  to  which  the  leakage  factor  of  a 


PREFACE.  Vll 

dynamo  can  be  estimated  from  the  dimensions  of  its  magnet 
frame  by  the  author's  formulae. 

A  small  portion  of  the  subject  matter  of  this  volume  first 
appeared  as  a  serial  entitled  "  Practical  Notes  on  Dynamo 
Calculation,"  in  the  Electrical  World,  May  19,  1894  (vol.  xxiii. 
p.  675)  to  June  8,  1895  (vol.  xxv.  p.  662),  and  reprinted  in 
the  Electrical  Engineer  (London),  June  i,  1894  (vol.  xiii.,  new 
series,  p.  640),  to  July  12,  1895  (vol.  xvi.  p.  43).  This  por- 
tion has  been  thoroughly  revised,  and  by  considering  all  the 
literature  that  has  appeared  on  the  subject  since  the  serial 
was  written  has  been  brought  to  date. 

It  has  been  the  aim  of  the  author  to  make  the  book  thor- 
oughly practical  from  beginning  to  end,  and  he  expresses  the 
hope  that  he  may  have  attained  this  end. 

The  author's  thanks  are  extended  to  all  those  firms  who 
upon  his  request  have  so  courteously  supplied  him  with  the 
data  of  their  latest  machines,  without  which  it  would  not  have 
been  possible  to  bring  this  work  up  to  date. 

Due  credit,  finally,  should  also  be  given  to  the  publishers, 
who  have  spared  neither  trouble  nor  expense  in  the  production 
of  this  volume. 

ALFRED  E.  WIENER. 

SCHENECTADY,   N.  Y., 

September  20,  1897. 


CONTENTS. 


LIST  OF  SYMBOLS, xxiii 

Part  I.  Physical  Principles  of  Dynamo-Electric  Machines. 

CHAPTER  I.    PRINCIPLES  OF  CURRENT  GENERATION  IN  ARMATURE. 
§ 

1.  Definition  of  Dynamo-Electric  Machinery,         .        .        .        .  3 

2.  Classification  of  Armatures,          .        »       '.        .-       .    •     .        .  4 

3.  Production  of  Electromotive  Force,     .       '.        ...        -.  4 

4.  Magnitude  of  Electromotive  Force,     ....        .        .  6 

5.  Average  Electromotive  Force,     .        .        ...        .        .  8 

6.  Direction  of  Electromotive  Force,       .  •                .        .        .        .  9 

7.  Collection  of  Currents  from  Armature  Coil,        .        .         .         .  12 

8.  Rectification  of  Alternating  Currents, 13 

9.  Fluctuations  of  Commutated  Currents,       ....        .        .  14 

Table  I.   Fluctuation  of  E.  M.  F.  of  Commutated 
Currents,        .        .        .        ;        .        ...       19 

CHAPTER  II.   THE  MAGNETIC  FIELD  OF  DYNAMO-ELECTRIC 
MACHINES. 

10.  Unipolar,  Bipolar,  and  Multipolar  Induction,     .         .        .  .      22 

11.  Unipolar  Dynamos,       .        .        .        .         .        .        .        .  -23 

12.  Bipolar  Dynamos,          .        .        .      '  .        .        .        .        .  .      26 

13.  Multipolar  Dynamos,     .        ...       .        .        ...  .       33 

14.  Methods  of  Exciting  Field  Magnetism,       ...        .      '.  -       35 

a.  Series  Dynamo,     .         .        .        .        .        r        ...       36 

b.  Shunt  Dynamo,     .         .         .         .         .         ...         .       37 

Table  II.  Ratio  of  Shunt  Resistance  to  Armature 
Resistance  for  Different  Efficiencies,          .        .      40 

c.  Compound  Dynamo,  .        .        .  .      .        .        .        .      41 

Part  II.  Calculation  of  Armature. 

CHAPTER  III.    FUNDAMENTAL  CALCULATION  FOR  ARMATURE 
WINDING.  . 

15.  Unit  Armature  Induction,    .        .        .        .        ...    .        .      47 

Table  III.  Unit  Induction,       .         ....'.      48 
Table  IV.  Practical   Values  of   Unit    Armature 

Inductions,  50 

ix 


x  CONTENTS. 

§  PAGE 

16.  Specific  Armature  Induction,        .        .        .        .        .        .        .       51 

17.  Conductor  Velocity 52 

Table  V.  Mean  Conductor  Velocities,    ...       52 

18.  Field  Density, 53 

Table  VI.  Practical  Field  Densities,  in  English 
Measure,  ........  54 

Table  VII.  Practical  Field  Densities,  in  Metric 
Measure,  .  .  .  .  .  ...  -54 

19.  Length  of  Armature  Conductor,  .        .       .-.        .        .        -55 

Table  VIII.  E.  M.  F.  Allowed  for  Internal  Resist- 
ances, .  .  .  ...  .  .  .  56 

20.  Size  of  Armature  Conductor,        .         .         .         .         ...       56 

CHAPTER  IV.    DIMENSIONS  OF  ARMATURE  CORE. 

21.  Diameter  of  Armature  Core,      ..     .v.        .        .     ,   .        .     •    .       58 

Table  IX.  Ratio  between  Core  Diameter  and 
Mean  Winding  Diameter  for  Small  Armatures,  59 

Table  X.  Speeds  and  Diameters  for  Drum  Arma- 
tures, .•  .  ..;.»..-  .••;«•  .  .  -. — ~-  .  60 

Table  XI.  Speeds  and  Diameters  for  High-Speed 
Ring  Armatures,  ....  .  .  .  .  .  60 

Table  XII.  Speeds  and  Diameters  for  Low-Speed 
Ring  Armatures,  .  ...  .  .  .  61 

22.  Dimensioning  of  Toothed  and  Perforated  Armatures,       .         .       61 

a.  Toothed  Armatures,     .        .        .        .        .        ...      65 

Table  XIII.  Number  of  Slots  in  Toothed  Arma- 
tures, .  .  .  .  .  .  .  .  .  66 

Table  XIV.  Specific  Hysteresis  Heat  in  Toothed 
Armatures,  for  Different  Widths  of  Slots,  .  69 

Table  XV.  Dimensions  of  Toothed  Armatures, 
English  Measure,  .  .'  .  .'  ...  •  .  70 

Table  XVI.  Dimensions  of  Toothed  Armatures, 
Metric  Measure,  ...  .  ...  .  .  71 

b.  Perforated  Armatures,          .....        .        ..       .       71 

23.  Length  of  Armature  Core,    .       ,.   .     „        .....         .        .       72 

a.  Number  of  Wires  per  Layer,       .        ...       •        •        •       72 

Table  XVII.  Allowance  for  Division-Strips  in 
Drum  Armatures,  .  .  .  .  73 

b.  Height  of  Winding  Space,  Number  of  Layers,  .    .    .      74 

Table  XVIII.  Height  of  Winding  Space  in  Arma- 
tures, .  -,  -  .  ••"'-.  .  .  .  .  -75 

c.  Total  Number  of  Conductors,  Length  of  Armature  Core,       76 

24.  Armature  Insulations,  .        .        .        .       •.        .        ...       78 

a.  Thickness  of  Armature  Insulations,  ....       78 

Table  XIX.  Thickness  of  Armature  Insulation  for 
Dynamos  of  Various  Sizes  and  Voltages,  .  .  82 


CONTENTS.  xi 

§  PAGE 

b.  Selection  of  Insulating  Material,         ."'•'".        .        .         .83 
Table  XX.  Resistivity   and   Specific    Disruptive 
Strength  of  Various  Insulating  Materials,          .      85 

CHAPTER  V.  FINAL  CALCULATION  OF  ARMATURE  WINDING, . 

25.  Arrangement  of  Armature  Winding,  .  '     .        .        .        .      87 

a.  Number  of  Commutator  Divisions,     .         .        .        .        .       87 

Table  XXI.  Difference  of  Potential  between  Com- 
mutator Divisions,         ......       88 

b.  Number  of  Convolutions  per  Armature  Division,      .         .       89 

c.  Number  of  Armature  Divisions,  .         .        .        .         .90 

26.  Radial  Depth  of  Armature  Core  Density  of  Magnetic  Lines  in 

Armature  Body, .  .  90 

Table  XXII.  Core  Densities  for  Various  Kinds  of 

Armatures,  .•.•••"••  •  •  91 
Table  XXIII.  Ratio  of  Net  Iron  Section  to  Total 

Cross-section  of  Armature  Core,          .        .        .  94 

27.  Total  Length  of  Armature  Conductor,  i .  •     .        .        .  94 

a.  Drum  Armatures,          .         .        .        ;         .         .        .         .       95 

Table  XXIV.    Ratio  between  Total  and  Active 
Length  of  Wire  on  Drum  Armatures,          .      .  .       96 

b.  Ring  Armatures,  .        .        .        ...        .         .       98 

c.  Drum-Wound  Ring  Armatures,  .        ...         .         -99 

Table  XXV.  Total  Length  of  Conductor  on  Drum- 
Wound  Ring  Armatures,      .        .        ,        .        .     100 

28.  Weight  of  Armature  Winding,     .        .        .        ,        .        .        .     100 

Table  XXVI.    Weight  of  Insulation   on   Round 
Copper  Wire,         .        .        .        .        .        .        .103 

29.  Armature  Resistance,  .        .        .  .        .        .        .        .     102 

CHAPTER  VI.  ENERGY  LOSSES  IN  ARMATURE.     RISE  OF 
ARMATURE  TEMPERATURE. 

30.  Total  Energy  Loss  in  Armature,         .        .        .  "     .        .        .     107 

31.  Energy  Dissipated  in  Armature  Winding,          ...        .     108 

Table  XXVII.  Total  Armature  Current  in  Shunt- 
and  Compound- Wound  Dynamos,       .        .        .     109 

32.  Energy  Dissipated  by  Hysteresis,       .         .      *.  -     .        .        .     109 

Table  XXVIII.  Hysteretic  Resistance  of  Various 

Kinds  of  Iron,        .        .        .        .        .        .        .     m 

Table  XXIX.  Hysteresis  Factors  for  Different 

Core  Densities,  English  Measure,  .  ...  113 
Table  XXX.  Hysteresis  Factors  for  Different 

Core  Densities,  Metric  Measure,  .  .  .115 
Table  XXXI.  Hysteretic  Exponents  for  Various 

Magnetizations,     .        .        .        .        ...        .116 

Table  XXXII.  Variation  of  Hysteresis  Loss  with 

Temperature, 118 


xii  CONTENTS.  » 

§  PAGE 

33.  Energy  Dissipated  by  Eddy  Currents, 119 

Table  XXXIII.  Eddy  Current  Factors  for  Differ- 
ent Core  Densities  and  for  Various  Laminations, 
English  Measure,  ......  120 

Table  XXXIV.  Eddy  Current  Factors  for  Differ- 
ent Core  Densities  and  for  Various  Laminations, 
Metric  Measure,  .......  122 

34.  Radiating  Surface  of  Armature,          .         .        .         .        .        .122 

a.  Radiating  Surface  of  Drum  Armatures,     .        .        .         .123 

Table  XXXV.  Length  of  Heads  in  Drum  Arma- 
tures   124 

b.  Radiating  Surface  of  Ring  Armatures,       .        .        .         .125 

35.  Specific  Energy  Loss,  Rise  of  Armature  Temperature,     .        .     126 

Table  XXXVI.  Specific  Temperature  Increase  in 
Armatures,  .  .  .  .  .  .  127 

36.  Empirical  Formula  for  Heating  of  Drum  Armatures,        .        .129 

37.  Circumferential  Current  Density  of  Armature,          .        .        .130 

Table  XXXVII.  Rise  of  Armature  Temperature 
Corresponding  to  Various  Circumferential  Cur- 
rent Densities,  .......  132 

38.  Load  Limit  and  Maximum  Safe  Capacity  of  Armature,    .        .     132 

Table  XXXVIII.  Percentage  of  Effective  Gap- 
Circumference  for  Various  Ratios  of  Polar  Arc,  135 

39.  Running  Value  of  Armatures,     ....    -.  .        .        .     135 

Table  XXXIX.  Running  Values  of  Various  Kinds 
of  Armatures,  .  .  .  •,-. •..-..-'..  .  ,  '.  .  136 

CHAPTER  VII.   MECHANICAL  EFFECTS  OF  ARMATURE 
WINDING. 

40.  Armature  Torque,         .        ,        •     ,    •        .       ...      ;~    ,    .>       .     137 

41.  Peripheral  Force  of  Armature  Conductors,         .  .        .     138 

42.  Armature  Thrust,          .        .        .        ,'.       .        ,'      ,        .        .     140 

CHAPTER  VIII.  ARMATURE  WINDING  OF  DYNAMO-ELECTRIC 
MACHINES. 

43.  Types  of  Armature  Winding, 143 

a.  Closed  Coil  Winding  and  Open  Coil  Winding,  .        .     143 

b.  Spiral  Winding,  Lap  Winding,  and  Wave  Winding,         .     144 

44.  Grouping  of  Armature  Coils,        .......     147 

Table  XL.  Symbols  for  Different  Kinds  of  Arma- 
ture Winding,  .  .  ..  .  .  .  .  150 

Table  XLI.  E.  M.  F.  Generated  in  Armature  at 
Various  Grouping  of  Conductors,  .  .  .151 

45.  Formula  for  Connecting  Armature  Coils,    .        .        ...     152 

a.  Connecting  Formula  and  its  Application  to  the  Different 

Methods  of  Grouping, 152 


CONTENTS.  xiii 

§  PAGE 

b.  Application  of  Connecting  Formula  to  the  Various  Prac- 
tical Cases,         .        .        .        .        . .•-••><• . .     .       ..        .     153 

46.  Armature  Winding  Data,      .        .        ,        v      ;.*        .        .        .     155 

a.  Series  Windings  for  Multipolar  Machines,         .        .        .155 

Table  XLII.    Kinds  of  Series  Winding  Possible  __ 
for  Multipolar  Machines,      .        .        .        .        .     156 

b.  Qualification  of  Number  of  Conductors  for  the  Various 

Windings,  ...        .        .        ...        ....     157 

Table  XLIII.  Number  of  Conductors  and  Con- 
necting Pitches  for  Simplex  Series  Drum  Wind- 
ings,   159 

Table  XLIV.    Number  of  Conductors  and  Con- 
necting Pitches  for  Duplex  Series  Drum  Wind- 
ing,         ..'     ,        ..        .'      ...        .         .         .     160 

Table  XLV.    Number  of  Conductors  and  Con- 
necting Pitches  for  Triplex  Series  Drum  Wind- 
ings,       .        ....        .     •    .        .        .         .     162 

Example  showing  use  of  Table  XLIII.,  .         .     158 

Example  showing  use  of  Tables  XLIV.  and  XLV. ,     162 
Example  of  Multiplex  Parallel  Windings,      .        .     167 

CHAPTER  IX.  DIMENSIONING  OF  COMMUTATORS,  BRUSHES,  AND 
CURRENT-CONVEYING  PARTS  OF  DYNAMO. 

47.  Diameter  and  Length  of  Commutator  Brush  Surface,       .        .     168 

48.  Commutator  Insulation,        .         .         .'•;,.        .        .        .     170 

Table  XL VI.  Commutator  Insulation  for  Various 
Voltages,  .  .  .  .  .  .  .171 

49.  Dynamo  Brushes, .171 

a.  Material  and  Kinds  of  Brushes, 171 

b.  Area  of  Brush  Contact,         .        .        .         .        .        .  174 

'  c.  Energy  Lost  in  Collecting  Armature-current;  Determina- 
tion of  Best  Brush-tension,       .        .        .        .        .        .176 

Table  XLVII.  Contact  Resistance  and  Friction 
for  Different  Brush  Tensions,  .  .  .  .179 

50.  Current-conveying  Parts,      .        .  .        .        .  .     181 

Table  XLVIII.  Current  Densities  for  Various 
Kinds  of  Contacts,  and  for  Cross-section  of  Dif- 
ferent Materials,  .  .  .  .  .  .183 

CHAPTER  X.   MECHANICAL  CALCULATIONS  ABOUT  ARMATURE. 

51.  Armature  Shaft,     .        .....".        .        .         .        .     184 

Table  XLIX.  Value  of  Constant  in  Formula  for 
Journal  Diameter  of  Armature  Shaft,  .  .185 

Table  L,  Value  of  Constant  in  Formula  for  Di- 
ameter of  Core  Portion  of  Armature  Shaft,  .  185 


XIV  CONTENTS. 

§  PAGE 

Table  LI.  Diameters  of  Shafts  for  Drum  Arma- 
tures,  186 

Table  LII.  Diameters  of  Shafts  for  High-Speed 
Ring  Armatures, 187 

Table  LIII.  Diameters  of  Shafts  for  Low-Speed 
Ring  Armatures,  .  .  .  .  .  .  .187 

52.  Driving  Spokes, 186 

53.  Armature  Bearings,       .........     190 

Table  LIV.  Value  of  Constant  in  Formula  for 
Length  of  Armature  Bearings,  .  .  .  .190 

Table  LV.  Bearings  for  Drum  Armatures,    .        .     191 

Table  LVI.  Bearings  for  High-Speed  Ring  Arma- 
tures, .  .  .  .  .  .  ....  192 

Table  LVII.  Bearings  for  Low-Speed  Ring  Arma- 
tures, .  .  '  :  .'  .  .  .,..'.  .  .  192 

54.  Pulley  and  Belt,     .        .        . 191 

Table  LVIII.  Belt  Velocities  of  High-Speed  Dy- 
namos of  Various  Capacities,       .         .         .     '   .     193 
Table  LIX.  Sizes  of  Belts  for  Dynamos,        .         .     194 

Part  III.  Calculation  of  Magnetic  Flux. 

CHAPTER  XI.  USEFUL  AND  TOTAL  MAGNETIC  FLUX. 

55.  Magnetic  Field,  Lines  of  Magnetic   Force,  Magnetic   Flux, 

Field  Density,     .        >  •      .        .        ......        .     199 

56.  Useful  Flux  of  Dynamo,       .         .         .         .         .         .         ...     200 

57.  Actual  Field  Density  of  Dynamo,        .         .       -.         .        .         .     202 

a.  Smooth  Armatures,       .        .         ...        .        .         .     204 

b.  Toothed  and  Perforated  Armatures,  .        ,        .        .     205 

58.  Percentage  of  Polar  Arc,      .        .  .        .        .       .»        .     207 

a.  Distance  between  Pole  Corners,         ..        .        .        .        .     207 

Table  LX.  Ratio  of  Distance  between  Pole  Cor- 
ners to  Length  of  Gap-Spaces  for  Various  Kinds 
and  Sizes  of  Dynamos,  .  .  .  .  .  208 

b.  Bore  of  Polepieces,        .         .        .         .        ...         .         .     209 

Table  LXI.  Radial  Clearance  for  Various  Kinds 

and  Sizes  of  Armatures,       .    ..,   ,        .  .'        .     209 

c.  Polar  Embrace,     .        .                 .        ...  .        .     210 

59.  Relative  Efficiency  of  Magnetic  Field,        .        .        .  .        .211 

Table  LXII.  Field  Efficiency  for  Various  Sizes 
of  Dynamos,  .  .  .  .  .  .  .  212 

Table  LXI II.  Variation  of  Field  Efficiency  with 
Output  of  Dynamo, 213 

Table  LXIV.  Useful  Flux  for  Various  Sizes  of 
Dynamos  at  Different  Conductor  Velocities,  .  214 

60.  Total  Flux  to  be  Generated  in  Machine,  .        .        .     214 


CONTENTS.  XV 

§  PAGE 

CHAPTER  XII.    CALCULATION  OF  LEAKAGE  FACTOR,  FROM 
DIMENSIONS  OF  MACHINE. 

A.  Formula  for  Probable  Leakage  Factor. 

61 .  Coefficient  of  Magnetic  Leakage  in  Dynamo-Electric  Machines,    2^7 - 

a.  Smooth  Armatures,      .        .        .        .        .        .        .        .217 

b.  Toothed  and  Perforated  Armatures,  .        .     •   .         .        .218 

Table  LXV.  Core  Leakage  in  Toothed  and  Per- 
forated Armatures,        .        .        .        .        .        .     219 

B.  General  Formula  for  Relative  Permeances. 

62.  Fundamental  Permeance  Formula  and  Practical  Derivations,      219 

a.  Two  Plane  Surfaces  Inclined  to  each  other,       .        .  .     220 

b.  Two  Parallel  Plane  Surfaces  Facing  each  other,       .  .     220 

c.  Two  Equal  Rectangular  Surfaces  Lying  in  one  Plane,  .     221 

d.  Two  Equal  Rectangles  at  Right  Angles  to  each  other,  .-     221 

e.  Two  Parallel  Cylinders,        .        .        .         .         .         .  .221 

/.  Two  Parallel  Cylinder-halves,     .        ...        .  .     223 

C.  Relative  Permeances  in  Dynamo-Electric  Machines. 

63.  Principle  of  Magnetic  Potential,  .        .        .        .        .   -     .     224 

64.  Relative  Permeance  of  the  Air  Gaps,  .         .        .        .         .     224 

a.  Smooth  Armature,        ...       ..        .        .        .        .     224 

Table  LXVI.  Factor  of  Field  Deflection  in  Dy- 
namos with  Smooth  Surface  Armatures,     .         .     225 

b.  Toothed  and  Perforated  Armature,    .        '.        .        .    '    .     227 

Table  LXVII.  Factor  of  Field  Deflection  in  Dy- 
namos with  Toothed  Armatures,         .        .  230 

65.  Relative  Average  Permeance  across  the  Magnet  Cores,   .        .231 

66.  Relative  Permeance  across  Polepieces,       .        .        .        .        .     238 

67.  Relative  Permeance  between  Polepieces  and  Yoke,  .        .     244 

D.  Comparison  of  Various  Types  of  Dynamos. 

68.  Application  of  Leakage  Formulae  for  Comparison  of  Various 

Types  of  Dynamos,    .        •.     •    .         .         .         .         .        .         .     248 

(1)  Upright  Horseshoe  Type,  .  •     .^. .     .        .        .     249 

(2)  Inverted  Horseshoe  Type,         .        ,*        .        .        .     250 

(3)  Horizontal  Horseshoe  Type,      .        .   ..  .'       .         .     251 

(4)  Single  Magnet  Type,       •,  *     >;.        .•       .         .         .251 

(5)  Vertical  Double  Magnet  Type,      ...        ..  •     .        .     252 

(6)  Vertical  Double  Horseshoe  Type,     .         .         .         .252 

(7)  Horizontal  Double  Horseshoe  Type,        .        .        .     253 

(8)  Horizontal  Double  Magnet  Type,     .         *  ...     .     254 

(9)  Bipolar  Iron-clad  Type,      .        .        .        ...     255 

(10)  Fourpolar  Iron-clad  Type,          .        ..:.•..     225 


xvi  CONTENTS. 

§  PAGE 

CHAPTER  XIII.    CALCULATION  OF  LEAKAGE  FACTOR,  FROM 
MACHINE  TEST. 

69.  Calculation  of  Total  Flux, 257 

a.  Calculation  of  Total  Flux  when  Magnet  Frame  Consists  of 

but  One  Material,      ........     259 

b.  Calculation  of  Total  Flux  when  Magnet  Frame  Consists  of 

Two  Different  Materials, 260 

70.  Actual  Leakage  Factor  of  Machine 261 

Table  LXVIII.  Leakage  Factors  for  Various 
Types  and  Sizes  of  Dynamos,  ....  263 

Part  IV.  Dimensions  of  Field-Magnet  Frame. 

CHAPTER  XIV.    FORMS  OF  FIELD-MAGNET  FRAMES. 

71.  Classification  of  Field-Magnet  Frames, 269 

72.  Bipolar  Types, 270 

73.  Multipolar  Types, 279 

74.  Selection  of  Type, ,        .  285 

CHAPTER  XV.    GENERAL  CONSTRUCTION  RULES. 

75.  Magnet  Cores, •      ,.        .     288 

a.  Material,        . .     288 

b.  Form  of  Cross-section^          .        .        .        .        .        «        .289 

Table  LXIX.  Circumference  of  Various  Forms  of 

Cross-sections  of  Equal  Area,      .        .        .   .     .  291 

c.  Ratio  of  Core  Area  to  Cross-section  of  Armature,      .        .  292 

76.  Polepieces, 293 

a.  Material, .        .  /     ..-,    .     293 

b.  Shape,    .         .        ,        ..         .         .     .    .        .        .'       .;      •     295 

77-  Base, .        .299 

78.  Zinc  Blocks,    .        .        *  .  "     .        .        .        .        .        .     300 

Table  LXX.  Height  of  Zinc  Blocks  for  High- 
Speed  Dynamos  with  Smooth-Core  Drum  Arma- 
tures, ..." .  301 

Table  LXXI.  Height  of  Zinc  Blocks  for  High- 
Speed  Dynamos  with  Smooth  Core  Ring  Arma- 
tures   .  .  ,  .  .302 

'  Table  LXXII.  Height  of  Zinc  Blocks  for  Low- 
Speed  Dynamos  with  Toothed  and  Perforated 
Armatures,  .  .  : 302 

Table  LXXIII.  Comparison  of  Zinc  Blocks  for 
Dynamos  with  Various  Kinds  of  Armatures,  .  303 

79.  Pedestals  and  Bearings,        . 303 

80.  Joints  in  Field-Magnet  Frame,     .         .        .        .        .        .        .305 

a.  Joints  in  Frames  of  One  Material,      .....     305 


CONTENTS.  xvii 

§  PAGE 

Table  LXXIV.    Influence  of  Magnetic   Density 

upon  the  Effect  of  Joints  in  Wrought  Iron,        .     307 
b.  Joints  in  Combination  Frames, 306 

CHAPTER  XVI.   CALCULATION  OF  FIELD-MAGNET  FRAME. 

81.  Permeability  of  Various  Kinds  of  Iron,  Absolute  and  Prac- 

tical Limits  of  Magnetization, 310 

Table  LXXV.  Permeability  of  Different  Kinds  of 

Iron  at  Various  Magnetizations,          .        .        .  311 
Table  LXXVI.  Practical  Working  Densities  and 

Limits  of  Magnetization  for  Various  Materials,  313 

82.  Sectional  Area  of  Magnet  Frame, 313 

Table  LXXVII.  Sectional  Areas  of  Field-Magnet 
Frame  for  High-Speed  Drum  Dynamos,  .  .  315 

Table  LXXVIII.  Sectional  Areas  of  Field-Magnet 
Frame  for  High-Speed  Ring  Dynamos,  .  .  315 

Table  LXXIX.  Sectional  Areas  of  Field-Magnet 
Frame  for  Low-Speed  Ring  Dynamos,  .  .316 

83.  Dimensioning  of  Magnet  Cores,  .        .        .,       .        .        .316 

a.  Length  of  Magnet  Cores,     .        .        .        .        .        .    "-  .     316 

Table  LXXX.  Height  of  Winding  Space  for  Dy- 
namo Magnets,  .  .  .  .  .  .  317 

Table  LXXXI.  Dimensions  of  Cylindrical  Magnet 
Cores  for  Bipolar  Types,  .  .  .  .  .  319 

Table  LXXXII.  Dimensions  of  Cylindrical  Mag- 
net Cores  for  Multipolar  Types,  .     .  *,       .     320 

Table  LXXXIII.  Dimensions  of  Rectangular 
Magnet  Cores  (Wrought  Iron  and  Cast  Steel),  .  321 

Table  LXXXIV.  Dimensions  of  Oval  Magnet 
Cores  (Wrought  Iron  and  Cast  Steel),  .  .  322 

b.  Relative  Position  of  Magnet  Cores,     .        .        .        .        .319 

Table  LXXXV.  Distance  between  Cylindrical 

Magnet  Cores,  .  .  .  .  .  .  .  32; 

Table  LXXXVI.  Distance  between  Rectangular 

and  Oval  Magnet  Cores,  .....  324 

84.  Dimensioning  of  Yokes 325 

85.  Dimensioning  of  Polepieces,        .        .        .         ....        .  325 

Table  LXXXVII.  Dimensions  of  Polepieces  for 
Bipolar  Horseshoe  Type  Dynamos,  .  .  .  326 

Part  V.  Calculation  of  Magnetizing  Force. 

CHAPTER  XVII.  THEORY  OF  THE  MAGNETIC  CIRCUIT. 

86.  Law  of  the  Magnetic  Circuit,       .         .        .        .     -  .        .        .     331 

87.  Unit  Magnetomotive  Force.     Relation  between  M.  M.  F.  and 

Exciting  Power,          .         .      *  .         .         .         .         .         .         .     332 


xvin  CONTENTS. 

§  PAGE 

88.  Magnetizing  Force  Required  for  any  Portion  of  a  Magnetic 

Circuit, 333 

Table   LXXXVIII.    Specific  Magnetizing  Forces 
for  Various  Materials  at  Different    Densities, 
in  English  Measure,      ......     336 

Table  LXXXIX.  Specific  Magnetizing  Forces  for 
Various  Materials,  at  Different  Densities,  in 
Metric  Measure, 337 

CHAPTER  XVIII.  MAGNETIZING  FORCES. 

Sg.  Total  Magnetizing  Force  of  Machine,        .        .     '.,,....  339 

90.  Ampere-Turns  for  Air  Gaps,      .......  339 

91.  Ampere-Turns  for  Armature  Core,    .        .        .        .        ...  340 

92.  Ampere-Turns  for  Field-Magnet  Frame,  .        ...  344 

93.  Ampere-Turns  for  Compensating  Armature  Reactions,  .        .  348 

Table  XC.  Coefficient  of  Brush  Lead  in  Toothed 
and  Perforated  Armatures,  ....  350 

Table  XCI.  Coefficient  of  Armature  Reaction 
for  Various  Densities  and  Different  Materials,  352 

94.  Grouping  of  Magnetic  Circuits  in  Various  Types  of  Dynamos,     353 


Part  VI.  Calculation  of  Magnet  Winding. 
CHAPTER  XIX.  COIL  WINDING  CALCULATIONS. 

95.  General  Formulae  for  Coil  Windings,         i        .        .        .        .     359 

96.  Size  of  Wire  Producing  Given  Magnetizing  Force  at  Given 

Voltage  between  Field  Terminals.     Current  Density  in  Mag- 
net Wire,  .        .        .        .        .  •      .        *        .        .        .     363 
Table  XGII.   Specific  Weights  of  Copper  Wire 
Coils,  Single  Cotton  Insulation,  .        .        .     367 

97.  Heating  of  Magnet  Coils,   .        .      ..'...:-       .        .      ,.     368 

Table  XCIII.  Specific  Temperature  Increase  in 
Magnet  Coils  of  Various  Proportions,  at  Unit 
Energy  Loss  per  Square  Inch  of  Core  Surface,  371 

98.  Allowable  Energy  Dissipation  for  Given  Rise  of  Temperature 

in  Magnet  Winding,  .        .        .'      .  •     ,       \        .        .        .     370 

CHAPTER  XX.  SERIES  WINDING. 

99.  Calculation  of  Series  Winding  for  Given  Temperature  In- 

crease,   374 

Table  XCIV.  Length  of  Mean  Turn  for  Cylin- 
drical Magnets,  . 375 

100.  Series  Winding  with  Shunt-Coil  Regulation 375 


CONTENTS.  xix 

§  PAGE 

CHAPTER  XXI.  SHUNT  WINDING. 

101.  Calculation  of  Shunt  Winding  for  Given  Temperature  In- 

crease,       383 

102.  Computation  of  Resistance  and  Weight  of  Magnet  Winding^    jj88_ 

103.  Calculation  of  Shunt  Field  Regulator,       .         .         .         .        .     390 

CHAPTER  XXII.  COMPOUND  WINDING. 

104.  Determination  of  the  Number  of  Shunt  and  Series  Ampere- 

Turns .  395 

Table  XCV.  Influence  of  Armature  Current  on 
Relative  Distribution  of  Magnetic  Flux,  .  .  398 

105.  Calculation  of  Compound  Winding  for  Given  Temperature 

Increase,      " .          .     399 

Part  VII.  Efficiency  of  Generators  and  Motors ; 
Designing  of  a  Number  of  Dynamos  of  Same 
Type ;  Calculation  of  Electric  Motors,  Unipolar 
Dynamos,  Motor-Generators,  etc.;  and  Dynamo- 
Graphics. 

.     CHAPTER  XXIII.  EFFICIENCY  OF  GENERATORS  AND  MOTORS. 

106.  Electrical  Efficiency,  .         .         .         .         .         .         .         .         .     405 

107.  Commercial  Efficiency,        .  '      .         .         .         ...         .     406 

Table  XCVI.  Losses  in  Dynamo  Belting,      .         .     409 

108.  Efficiency  of  Conversion,     .         ...        ...         .         .     409 

109.  Weight-Efficiency  and  Cost  of  Dynamos,          -.        .        :  '      .     410 

Table  XCVII.  Average  Weight  and  Cost  of  Dy- 
namos,   .        .        .        .        .        .,       .        .        .     412 

CHAPTER  XXIV.  DESIGNING  OF  A  NUMBER  OF  DYNAMOS  OF 

SAME  TYPE. 

no.  Simplified  Method  of  Armature  Calculation,     .        .  .     413 

in.  Output  as  a  Function  of  Size,     .         .        .  .        .        .     416 

Table  XCVIII.  Exponent  of  Output-Ratio  in 
Formula  for  Size-Ratio,  for  Various  Combina- 
tions of  Potentials  and  Sizes,  .  .  .  .417 

CHAPTER  XXV.  CALCULATION  OF  ELECTRIC  MOTORS. 

112.  Application  of  Generator  Formulae  to  Motor  Calculation,       .     419 

Table  XCIX.  Average  Efficiencies  and  Electrical 

Activity  of  Electric  Motors  of  Various  Sizes,     .  422 

113.  Counter  E.  M.  F '.        .        .        .        .  423 

114.  Speed  Calculation  of  Electric  Motors,        .        i  -    •  .        .        .  424 

Table  C.  Tests  on  Speed  Variation  of  Shunt 
Motors, 427 


xx  CONTENTS. 

§  PAGE 

115.  Calculation  of  Current  for  Electric  Motors,       ....  427 

a.  Current  for  any  Given  Load, 427 

b.  Current  for  Maximum  Commercial  and  Electrical  Effi- 

ciency,       .        .        .        .        .        .        .                 .        .  428 

116.  Designing  of  Motors  for  Different  Purposes,    ....  429 

Table  CI.  Comparison  of  Efficiencies  of  Two  Mo- 
tors Built  for  Different  Purposes,        .        .        .  430 

117.  Railway  Motors, 431 

a.  Railway  Motor  Construction, 431 

(1)  Compact  Design  and  Accessibility,   ....  432 

(2)  Maximum  Output  with  Minimum  Weight,        .         .  432 

(3)  Speed,  and  Reduction-Gearing,          ....  433 

Table  CII.  General  Data  of  Most  Common  Rail- 
way Motors,  .....'...  435 

(4)  Speed  Regulation, 436 

(5)  Selection  of  Type,        .         .         .         .         .         .         .  437 

b.  Calculations  Connected  with  Railway  Motor  Design,       .  438 

(1)  Counter  E.  M.  F.,  Current,  and  Energy  Output  of 

Motor, 438 

(2)  Speed  of  Motor  for  Given  Car  Velocity,    .        .        .  439 

(3)  Horizontal  Effort  and  Capacity  of  Motor  Equipment 

for  Given  Conditions, «44O 

Table  CIII.  Specific  Propelling  Power  Required 

for  Different  Grades  and  Speeds,     .        .        .  441 
Table  CIV.  Horizontal  Effort  of  Motors  of  Vari- 
ous Capacities  at  Different  Speeds,          .        .  442 

(4)  Line  Potential  for  Given  Speed  of  Car  and  Grade  of 

Track, 442 

CHAPTER  XXVI.  CALCULATION  OF  UNIPOLAR  DYNAMOS. 

118.  Formulae  for  Dimensions  Relative  to  Armature  Diameter,     .  443 

119.  Calculation  of  Armature  Diameter  and  Output  of  Unipolar 

Cylinder  Dynamo .        ..  446 

120.  Formulae  for  Unipolar  Double  Dynamo, 449 

121.  Calculation  for  Magnet  Winding  for  Unipolar  Cylinder  Dy- 

namos,      .        •        .        .        .        .        -        .        ...  450 

CHAPTER  XXVII.   CALCULATION  OF  MOTOR-GENERATORS  ; 
GENERATORS  FOR  SPECIAL  PURPOSES,  ETC. 

122.  Calculation  of  Motor-Generators,      •;• 452 

123.  Designing  of  Generators  for  Special  Purposes,         .        .        -455 

a.  Arc  Light  Machines  (Constant-Current  Generators),        .  455 

b.  Dynamos  for  Electro-Metallurgy,        .....  459 

c.  Generators  for  Charging  Accumulators 461 

d.  Machines  for  Very  High  Potentials, 462 

124.  Prevention  of  Armature  Reaction, 463 

a.  Ryan's  Balancing  Field  Coil  Method,         .        .        .        .  464 


CONTENTS.  xxi 

§  PAGE 

b.  Sayers'  Compensating  Armature  Coil  Method,          .        .     467 

c.  Thomson's  Auxiliary  Pole  Method, 469 

125.  Size  of  Air  Gaps  for  Sparkless  Collection,         ....     470 

126.  Iron  Wire  for  Armature  and  Magnet  Winding,        .        .        .     472 

CHAPTER  XXVIII.  DYNAMO  GRAPHICS. 

127.  Construction  of  Characteristic  Curves,      .        ,    •   •;  ' '     .        .     476 

Table  CV.  Factor  of  Armature  Ampere-Turns  for 

Various  Mean  Full-Load  Densities,     .     '    .        .     480 
Practical  Example,          '.         ;        .        .      •  .         .     481 

128.  Modification  in  the  Characteristic  Due  to  Change  of  Air  Gap,     483 

129.  Determination  of  the  E.  M.  F.  of  a  Shunt  Dynamo  for  a 

Given  Load,       .        .         .        .         .         .        .         ...     485 

130.  Determination  of  the  Number  of  Series  Ampere-Turns- for  a 

Compound  Dynamo,        .        .        <        .        .       .,        .        .     486 

131.  Determination  of  Shunt  Regulators,          ...        ...        .     487 

a.  Regulators  for  Shunt  Machines  of  Varying  Load,  .     487 

Practical  Example,  .         .         .  .         .         .     488 

b.  Regulators  for  Shunt  Machines  of  Varying  Speed,  .         .     490 

Practical  Example,   . 492 

c.  Regulators  for  Shunt  Machines  of  Varying  Load    and 

Varying  Speed,         .        .        ...        .    • '  i,         .        .  493 

Practical  Example,  .        ....        .        .  495 

d.  Regulators  for  Varying  the  Potential  of  Shunt  Dynamos,  496 

132.  Transmission  of  Power  at  Constant  Speed  by  Means  of  Two 

Series  Dynamos,    • '      .        .        .        .     497 

133.  Determination  of  Speed  and  Current  Consumption  of  Rail- 

way Motors  at  Varying  Load,         ,        .        .      •  .        .         ,     500 
Practical  Example,  .        .  .         .     501 

Part  VIII.  Practical  Examples  of  Dynamo 
Calculation. 

CHAPTER  XXIX.  EXAMPLES  OF  CALCULATIONS  FOR  ELECTRIC 
GENERATORS. 

134.  Calculation  of  a  Bipolar,  Single  Magnetic  Circuit,  Smooth 

Ring,  High-Speed  Series  Dynamo  (10  KW.    Single  Magnet 
Type.     250  V.     40  Amp.     1200  Revs.),         .        .        .        .     505 

135.  Calculation  of  Bipolar,   Single    Magnetic   Circuit,    Smooth 

Drum,   High-Speed   Shunt  Dynamo  (300  KW.      Upright 
Horseshoe  Type.     500  V.     600  Amp.     400  Revs.),        I        .     527 

136.  Calculation  of  a  Bipolar,  Single  Magnetic  Circuit,  Smooth 

Drum,  High-Speed,   Compound  Dynamo  (300  KW.      Up- 
right Horseshoe  Type.     500  V.    600  Amp.     400  Revs.),       .     547 

137.  Calculation  of  a  Bipolar  Double  Magnetic  Circuit,  Toothed 

Ring,  Low-Speed  Compound  Dynamo  (50  KW.     Double 
Magnet  Type.     125  V.     400  Amp.     200  Revs.),     .  .     552 


xxii  CONTENTS. 

§  PAGE 

138.  Calculation  of  a  Multipolar,  Multiple  Magnet,  Smooth  Ring, 

High-Speed  Shunt  Dynamo  (1200  KW.  Radial  Innerpole 
Type.  10  Poles.  150  V.  8000  Amp.  232  Revs.),  .  .  566 

139.  Calculation  of  a  Multipolar,  Single  Magnet,  Smooth  Ring, 

Moderate-Speed  Series  Dynamo '  (30  KW.  Single  Magnet 
Innerpole  Type.  6  Poles.  600  V.  50  Amp.  400  Revs.),  580 

140.  Calculation  of  a  Multipolar,  Multiple  Magnet,  Toothed  Ring, 

Low-Speed  Compound  Dynamo  (2000  KW.  Radial  Outer- 
pole  Type.  16  Poles.  540  V.  3700  Amp.  70  Revs.),  .  587 

141.  Calculation  of  a  Multipolar,   Consequent  Pole,   Perforated 

Ring,  High-Speed  Shunt  Dynamo  (100  KW.  Fourpolar 
Iron-Clad  Type.  200  V.  500  Amp.  600  Revs.),  in  Metric 
Units,  .  .  .  .  .  .  .  .  .  .  .  603 

CHAPTER  XXX.  EXAMPLES  OF  LEAKAGE  CALCULATIONS, 
ELECTRIC  MOTOR  DESIGN,  ETC. 

142.  Leakage  Calculation  for  a  Smooth  Ring,  One-Material  Frame, 

Inverted  Horseshoe  Type  Dynamo  (9.5  KW.  "Phoenix" 
Dynamo:  105  V.  90  Amp.  1420  Revs.),  .  .  *  : .  614 

143.  Leakage  Calculation  for  a  Smooth  Ring,  One-Material  Frame, 

Double  Magnet  Type  Dynamo  (40  KW.  "  Immisch  "  Dy- 
namo: 690  V.  59  Amp.  480  Revs.),  .  .  ..,..'.  .  618 

144.  Leakage    Calculation    for    a    Smooth    Drum,    Combination 

Frame,  Upright  Horseshoe  Type  Dynamo  (200  KW.  "  Ed- 
ison" Bipolar  Railway  Generator:  500  V.  400  Amp.  450 
Revs.),  .  .  .  .  .  .  ...  .  .  '  .  621 

145.  Leakage  Calculation    for    a    Toothed    Ring,    One-Material 

Frame,  Multipolar  Dynamo  (360  KW.     "  Thomson-Hous- 
ton"   Fourpolar    Railway  Generator:    600  V.     600    Amp. 
400  Revs.),         .        .        „        .        *    H    .        ....     624 

146.  Calculation  of  a  Series  Motor  for  Constant- Power  Work  (In- 

verted Horseshoe  Type.     25  HP.     220  V.     850  Revs.),        .     628 

147.  Calculation  of  a  Shunt  Motor  for  Intermittent  Work  (Bipolar 

Iron-Clad  Type.     15  HP.     125  V.     1400  Revs.),    .        .        .     637 

148.  Calculation  of  a  Compound  Motor  for  Constant  Speed  at 

Varying  Load  (Radial  Outerpole  Type.  4  Poles.     75  HP. 

440  V.     500  Revs.),   .        .        .        .        .      °  .        .        .        .     644 

149.  Calculation  of  a  Unipolar  Dynamo  (Cylinder  Single  Type. 

300  KW.     10  V.     30,000  Amp.     looo  Revs.),          .        .         .     652 

150.  Calculation  of  a  Motor-Generator  (Bipolar  Double  Horseshoe 

Type,  si  KW.  1450  Revs.  Primary:  500  V.  n  Amp. 
Secondary:  noV.  44  Amp.),  .  .  .  ...  655 

INDEX,   .        .        .        .  661 


LIST  OF  SYMBOLS. 


Throughout  the  book  a  uniform  system  of  notation,  based 
upon  the  standard  Congress-notation,  is  adhered  to,  the  same 
quantity  always  being  denoted  by  the  same  symbol.  The  fol- 
lowing is  a  complete  list  of  these  symbols,  here  compiled  for 
convenient  reference: 

AT,  at  =  ampere-turns. 

AT  —  total  number  of  ampere-turns  on  magnets,  at  normal 

load,  or  magnetizing  force. 
A T'  —  total  magnetizing  force  required  for  maximum  output 

of  machine. 
AT"  =  total  magnetizing  force  required  for  minimum  output 

of  machine. 
^  =  total  magnetizing  force  required  for  maximum  speed 

of  machine. 
=  total  magnetizing  force  required  for  minimum  speed 

of  machine. 

AT0  =  total  magnetizing  force  required  at  open  circuit. 
at&  =   magnetizing  force  required   for  armature  core,  normal 

load. 
at&0  =  magnetizing   force   required    for   armature   core,   open 

circuit. 
atci  =  magnetizing   force    required  for  cast  iron    portion    of 

magnetic  circuit,  normal  load. 
0/0<Le    =  magnetizing  force  required  for  cast  iron  portion   of 

magnetic  circuit,  no  load. 
atc^  =  magnetizing  force  required  for  cast  steel  portion  of 

magnetic  circuit,  normal  load. 
atCSo  =  magnetizing  force  required   for   cast  steel   portion  of 

magnetic  circuit,  no  load. 

atK  =  magnetizing  force  required   for  air  gaps,  normal   load. 
atKo  =  magnetizing  force  required  for  air  gaps,  open  circuit. 


xxiv  LIST  OF  SYMBOLS, 

tf/g.a.r.   =   combined  magnetizing  force  required  for  air  gaps, 

armature  core,  and  reactions. 
atm  =  magnetizing  force  required  for  magnet  frame,  normal 

output. 
atmo  =  magnetizing  force  required  for   magnet   frame,    open 

circuit. 

atv,  afpo  =  magnetizing  forces  required  for  polepieces. 
atT  —  magnetizing  force  required  for  compensation  of  armature 

reactions. 
ats  =  magnetizing  force  required  to  produce  a  reversing  field 

of  sufficient  strength  for  sparkless  collection. 
atwA  =  magnetizing  force  required  for  wrought  iron  portion  of 

magnetic  circuit,  normal  load. 
«r/wio  =  magnetizing  force  required  for  wrought  iron   portion 

of  magnetic  circuit,  no  load. 

aty,  atyo  =  magnetizing  forces  required  for  yoke,  or  yokes. 
a  =  half  pole-space  angle  (also  angle  of  brush-displacement). 
(B  =  magnetic  flux  density  in  magnetic  material,  in  lines  per 

square  centimetre. 
(B"  =  magnetic  flux  density  in  magnetic  material,  in  lines  per 

square  inch. 

&a»  ®"a  —  average  density  of  magnetic  lines  in  armature  core. 
®ai>  ®"ai  =  maximum  density  of  magnetic  lines  in  armature 

core. 
(Baa,  (B"a2  —  minimum  density  of  magnetic  lines   in   armature 

core. 
(Bc>i.,  (B"c.i.  =  mean  density  of  magnetic  lines  in  cast  iron  portion 

of  frame. 
<BC.S.,(B"C.S.  =  mean  density  of  magnetic  lines  in  cast  steel  portion 

of  frame. 

(&p,  (B"p  =  mean  density  of  magnetic  lines  in  polepieces. 
<BP1,  (B"P1  =  maximum  density  of  magnetic  lines  in  polepieces. 
(BP2,  (B"P3  =  minimum  magnetic  density  in  polepieces. 
(Bt,  <&"t  =  magnetic  density  in  armature  teeth. 
<Bw>i,  (&"w.i.—  magnetic  density  in  wrought  iron  portion  of  mag- 
netic circuit. 
b  —  breadth,  width. 
b&  =  breadth  of  armature   cross-section,    or  radial   depth   of 

armature  core. 
b\  =  maximum  depth  of  armature  core. 


LIST  OF  SYMBOLS.  XXV 

bb  —  width  of  commutator  brush. 

6E  =  breadth  of  belt. 

^k  =  circumferential  breadth  of  brush  contact. 

bs  =  width  of  armature  slot. 

b's  ==  available  width  of  armature  slot. 

b"s  —  width  of  armature  slot  for  minimum  tooth-density. 

^s  =  smallest  breadth  of  armature  spoke  (parallel  to  shaft). 

bt  =  width,  at  top,  of  armature  tooth. 

b\  =  radial  depth  to  which  armature  tooth  is  exposed  to  mag- 
netic field. 

b\  —  width,  at  root,  of  armature  tooth. 

by=  breadth  of  yoke. 

fj  —  angle  embraced  by  each  pole. 

/?j  =  percentage  of  polar  arc. 

/3\  =  percentage  of  effective  arc,  or  effective  field  circum- 
ference. 

Y  =  electrical  conductivity,  in  mhos. 

Z>,  d,  6  =  diameter. 

Z>m  =  external  diameter  of  magnet  coil. 

Z)p  =  diameter  of  armature  pulley. 

d&  =  diameter  of  armature  core. 

d'&  =  mean  diameter  of  armature  winding. 

d1 \  =  external  diameter  of  armature  (over  winding). 

d'"&  —  mean  diameter  of  armature  core. 

*/b  =  diameter  of  armature  bearings. 

dc  —  diameter  of  core-portion  of  armature  shaft. 

dt  —  mean  diameter  of  magnetic  field. 

dh  —  diameter  of  front  head  of  (drum)  armature. 

d'h  —  diameter  of  back  head  of  (drum)  armature. 

</k  =  diameter  of  commutator. 

dm  =  diameter  of  magnet  core. 

dp  =  diameter  of  bore  of  polepieces. 

//w  =  diameter  of  car  wheel,  in  inches. 

#a  =  diameter  of  armature  wire,  in  mils. 

6'&  =  width  of  insulated  armature  conductor,  in  inches. 

d"&  =  height  of  insulated  armature  conductor,  in  inches. 

<y"'a  =  pitch  of  conductors  on  armature  circumference. 

#i  =  thickness  of  iron  laminae  in  armature  core,  in  inches. 

6m  =  diameter  of  magnet  wire,  bare,  in  mils. 

<S'm  =  diameter  of  magnet  wire,  insulated,  in  mils. 


XXVI  LIST  OF  SYMBOLS. 

tfge  =  diameter  of  series  field  wire. 

#8h  =  diameter  of  shunt  field  wire. 

(#a)2  =  sectional  area  of  armature  conductor,  in  circular  mils. 

(^a)Smm  —  sectional    area   of   armature    conductor    in    square 

millimetres. 
(#ai)2  =  sectional  area   of   single   armature   wire,    in  circular 

mils. 

,£",<?  =  electromotive  force,  or  pressure,  in  volts. 
E  —  normal  E.  M.  F.    output,   or  voltage,  of  generator;  ter- 
minal E.  M.  F.,  or  supply  voltage  of  motor. 
E'  =  total  E.  M.  F.  induced  in  armature  of  generator;  counter 

E.  M.  F.  of  motor. 

E0  =  total  E.  M.  F.  active  in  armature,  on  open  circuit. 
E^  —  total  E.  M.  F.  active  in  armature,  at  minimum  load. 
Et  =  total  E.  M.  F.  active  in  armature,  at  maximum  load. 
Em  =  E.  M.  F.  between  terminals  of  magnet  winding. 
e  —  unit  armature  induction  per  pair  of  poles,  volts  per  foot. 
el  =  unit  armature  induction  per  pair  of  poles,  volts  per  metre. 
e'  —  specific  induction  of  active  armature  conductor,  volts  per 

foot. 
e\  —  specific  induction  of  active  armature  conductor,  volts  per 

metre. 
e"  —  specific  generating  power  of  motor,  /.  e.,  volts  of  counter 

E.  M.  F. ,  produced  at  a  speed  of  i    revolution  per 

minute. 
e^  =  volts  generated  per  100  conductors,  per  100  revolutions 

per  minute,  and  i  megaline  of  flux  per  pole. 
<?3  =  average  volts  between  commutator  segments  per  megaline 

and  per  100  revolutions  per  minute. 
e&  —  drop  of  voltage  due  to  armature  resistance. 
e  =  factor  of  eddy  current  loss  in  armature,  English  measure 

(watts  per  cubic  foot). 
e'  =  factor  of  eddy  current  loss  in  armature,  metric  measure 

(watts  per  cubic  metre). 
£x  =  eddy  current  constant. 
$  =  magneto-motive  force,  in  gilberts. 
F,  f  =  force,  or  pull,  in  pounds. 
F&  — •  total  peripheral  force  of  armature,  in  pounds. 
P'A  —  peripheral  force  corresponding  to  safe  working  strength 

of  armature  spokes,  in  pounds. 


LIST  OF  SYMBOLS.  xxvil 

F^  =  tension  on  tight  side  of  belt,  in  pounds. 

Fv  =  pull  at  pulley  circumference,  in  pounds. 

/a  =  peripheral  force  per  armature  conductor,  in  pounds. 

/B  =  tension  on  slack  side  of  belt,  in  pounds. 

fh  =  horizontal  effort,  or  draw-bar  pull  of  railway  motor. 

/k  =  specific  tangential  pull  due  to  brush-friction,  at  1000  feet 
per  second,  in  pounds  per  square  inch  of  contact 
area. 

/'k  =  specific  tangential  pull  due  to  brush-friction,  at  any 
velocity,  in  pounds  per  square  inch  of  contact  area. 

ft  =  armature  thrust,  /.  e. ,  displacing  force  acting  on  arma- 
ture due  to  unsymmetrical  field. 

/((E)  =  function  of  (B;  magnetizing  force  per  centimetre 
length  for  density  (B. 

/((B")  =  function  of  (B";  magnetizing  force  per  inch  length 
for  density  (ft". 

/  (®a)>  /  ((B"a)  =  specific  magnetizing  force  of  armature  core. 

/  ((Bt..i.),  /  ((B"c.i.)  =  specific  magnetizing  force  of  cast  iron  por- 
tion of  magnetic  circuit. 

/((Bc.s.)>  /(®"c.s.)  =  specific  magnetizing  force  of  cast  steel  por- 
tion of  magnetic  circuit. 

f  (®P)>  f  (®"P)  —  specific  magnetizing  force  of  polepieces. 

/  (®t)>  /  (®"t)   =  specific  magnetizing  force  of  armature  teeth. 

/  (®w.i.)>  /  (®"w.i.)  =  specific  magnetizing  force  of  wrought  iron 
portion  of  magnetizing  circuit. 

/  ((By),  /  (<B"y)  =  specific  magnetizing  force  of  yoke. 

<£  =  useful  flux,  /.  e.y  number  of  lines  of  force  cutting  arma- 
ture conductors,  at  normal  output. 

#0  —  useful  flux,  /.  e.,  number  of  lines  of  force  cutting  arma- 
ture conductors,  at  open  circuit. 

0'  =  total  flux,  or  total  number  of  lines  generated,  at  normal 
output  (webers). 

<&"  =  total  flux  per  magnetic  circuit. 

#'p  —  relative  efficiency  of  magnetic  field  (webers  per  watt  of 
output  at  unit  conductor  velocity). 

g  =  grade  of  railway  track,  in  per  cent. 

3C  =  magnetic  flux  density  in  air,  or  field  density,  in  gausses 
(lines  of  force  per  square  centimetre). 

3C"  =  field  density,  in  lines  of  force  per  square  inch. 

3C1?  3C*,  —  density  on  stronger  side  of  an  unsymmetrical  field. 


xxvill  LIST  OF  SYMBOLS. 

3C2 ,  3C"2  —  density  on  weaker  side  of  an  unsymmetrical  field. 

h  =  height,  thickness. 

h&  —  total  height  of  winding  space  in  armature  (depth  of  slots). 

h'&  =  available  height  of  armature  winding  space. 

h^  =  thickness  of  belt,  in  inches. 

hc  —  radial  height  of  clearance  between  external  diameter  of 

finished  armature  and  polepieces. 
hi  =  thickness  of  commutator  side  insulation,  inch. 
h\  =  thickness  of  commutator  bottom  insulation,  inch. 
h\  —  thickness  of  commutator  end  insulation,  inch. 
/im  =  height  of  winding  space  on  field  magnets. 
h'm  —  net  height  of  field  winding. 
/£p  =  height  of  polepieces. 
hs  =  smallest  thickness  of  armature  spoke   (perpendicular  to 

shaft). 

hy  —  height  of  yoke. 
hz  =  height  of  zinc  block. 
HP,  hp  =  horse  power. 
rj  —  factor  of  hysteresis  loss  in  armature,   English    measure 

(watts  per  cubic  foot). 
rf  =  factor  of  hysteresis  loss   in   armature,    metric   measure 

(watts  per  cubic  metre). 
T/J  —  hysteretic  resistance. 
rf0  =  commercial  efficiency. 
rjQ  —  electrical  efficiency. 

rjg  =  gross  efficiency,  or  efficiency  of  conversion. 
/,  /  =  intensity  of  current,  amperes. 

/=  current  output,  or  amperage,  of  generator;  current  sup- 
plied to  motor  terminals. 
/'  —  total  current  active  in  armature. 
/,,/„,...  =  currents  flowing  in  coils  /,   //,...  of  series 

field  regulator. 

/m  =  current  in  magnet  winding. 
/gg  =  total  series  current,  in  amperes. 
78h  ~  total  shunt  current,  in  amperes. 
/a  =  current  density  in  armature  conductor,  circular  mils  per 

ampere. 
fe  =  circumferential  current  density  of  armature  (amperes  per 

unit  length  of  core  circumference). 
/m  =  current  density  in  magnet  wire,  circular  mils  per  ampere. 


LIST  OF  SYMBOLS.  XXIX 

./ae  =  current  density  in  series  wire,  circular  mils  per  ampere. 
/sh  =  current  density  in  shunt  wire,  circular  mils  per  ampere. 
K,  k  —  constants. 
£j ,  £a ,  £3,  .  .  .  —  various  constants  depending  upon  material, 

manner  of  manufacture,  and  similar  conditions. 
Z,  /  =  length,  distance. 
Za  =  active  length  of  armature  conductor. 
Ze  =  effective  length  of  armature  conductor. 
Zm  =  total  length  of  magnet  wire,  in  feet. 
Zse  =  total  length  of  series  wire,  in  feet. 
Zsh  =  total  length  of  shunt  wire,  in  feet. 
Zt  —  total  length  of  armature  conductor. 
4  =  length  of  armature  core. 
l\  —  length  of  magnetic  circuit  in  armature  core. 
4  —  length  of  armature  bearings. 

/'b  —  length  of  gap  between  adjacent  commutator  brushes. 
4  =  total  length  of  commutator  brush  contact  surface. 
/"ci  =  length  of  magnetic  circuit  in  cast  iron  portion  of  field 

frame. 
l"cs  =  length  of  magnetic  circuit  in  cast  steel  portion  of  field 

frame. 

4  =  mean  length  of  magnetic  field. 
l"g  =  length  of  magnetic  circuit  in  air  gaps. 
4  =  length  of  (drum)  armature  heads. 

4  =  effective  axial  length  of  commutator  brush  contact  sur- 
face. 

/m  —  length  of  magnet  core. 
/'m  =  total  length  of  magnet  cores. 
I"m  =  total  length  of  magnetic  circuit  in  entire  field  magnet 

frame. 

/p  —  length  of  polepieces,  parallel  to  armature  inductors. 
/'p  =  mean  distance  between  pole-corners. 
/"p  =  length  of  magnetic  circuit  in  polepieces. 
4  =  distance  of  smallest  armature  spoke  section  from  active 

conductors,  or  leverage  at  smallest  section  of  armature 

spokes. 

/t  =  mean  length  of  turn  of  field  magnet  winding,  in  feet. 
7T  —  mean  length  of  turn  of  field  magnet  winding,  in  inches. 
/'T  =  length  of  mean  series  turn. 
'%  =  length  of  mean  shunt  turn. 


XXX  LIST  OF  SYMBOLS. 

/"wi  =  length  of  magnetic  circuit  in  wrought  iron  portion  of 
field  frame. 

l'y  =  length  of  yoke. 

l"7  —  length  of  magnetic  circuit  in  yoke. 

A  =  factor  of  magnetic  leakage. 

A/  —  factor  of  core  leakage  in  machines  with  toothed  or  per- 
forated armature. 

Am  =         =  specific  length  of  magnet  wire,  in  feet  per  ohm. 

/An 

A/m  —  specific  length  of  magnet  wire,  in  feet  per  pound. 

Age  =  specific  length  of  series  wire,  in  feet  per  ohm. 

Ash  —  specific  length  of  shunt  wire,  in  feet  per  ohm. 

M,  M1 ,  .  .  .  =  mass,  volume. 

M  —  mass  of  iron  in  armature  core,  in  cubic  feet. 

Af1  —  mass  of  iron  in  armature  core,  in  cubic  metres. 

M\  —  mass  of  iron  in  armature  core,  in  cubic  centimetres. 

J/"m  =  volume  of  coil  space  on  field  magnets,  in  cubic  inches. 

[A.  =  magnetic  permeability. 

JV,  n  =  number.  4 

JV  =  number  of  revolutions  of  armature  per  minute. 

N'  =  number  of  revolutions  of  armature  per  second. 

JVl  =  frequency  of  magnetic  reversals,  or  number  of  cycles 
per  second. 

JV^  =  speed  of  dynamo,  when  run  as  motor. 

JV&  —  total  number  of  turns  on  armature. 

JVe  =  number  of  conductors  around  pole-facing  circumference 
of  armature. 

JVm  =  number  of  turns  on  magnets. 

JVse  =  number  of  series  turns. 

N^  —  number  of  shunt  turns. 

n  =  speed  ratio,  i.  <?.,  abnormal  divided  by  normal  speed  of 
machine. 

n^  =  speed  ratio  for  maximum  speed. 

«2  =  speed  ratio  for  minimum  speed. 

n&  =  number  of  turns  per  armature  coil. 

«b  =  number  of  commutator  brushes,  at  one  point  of  commu- 
tation. 

nc  =  number  of  armature  coils,  or  number  of  commutator 
divisions. 

n'c  =  number  of  armature  slots. 


LIST  OF  SYMBOLS.  XXXI 

n#  =  number  of  wires  stranded  in  parallel  to  make  up   one 

armature  conductor. 

n{  —  number  of  separate  field  coils  in  each  magnetic  circuit. 
72k   —   number   of   commutator   bars   covered   by   one   set  of 

brushes. 

;/!  =  number  of  layers  of  wire  on  armature. 
nm  —  number  of  independent  armature  windings  in  multiple. 
72p  =  number  of  pairs  of  magnet  poles. 
«'p  =  number  of  pairs  of  parallel  branches  in   armature,    or 

number  of  bifurcations  of  current  in  armature. 
n\  =  number  of  pairs  of  brush  sets. 

nr  =  number  of  steps,  or  divisions,  in  shunt  field  regulator. 
ns  =  number  of  armature  circuits  connected  in  series  in  each 

of  the  parallel  branches. 

ns  =  total  number  of  spokes  in  armature  spiders. 
nae  =  number  of  wires  constituting  one  series  field  conductor. 
«w  =  number  of  armature  wires  per  layer. 
nz  —  number  of  magnetic  circuits  in  dynamo. 
%  $t ,  ^ ,  .  .  .  =  permeances. 
^  —  relative  permeance  of  gap-spaces. 
$2  =  relative  average  permeance  across  magnet  cores. 
^3  =  relative  permeance  across  polepieces. 
<$4  =  relative  permeance  between  polepieces  and  yoke. 
fB'  =  relative  permeance  of  clearance  space  between  poles  and 

external  surface  of  armature. 
($"  =  relative  permeance  of  teeth. 
!B'"  =  relative  permeance  of  slots. 
P  =  electrical  energy  at  terminals  of  machine;  i.  <r.,  output 

of  generator,  intake  of  motor. 
P'  —  total  electrical  energy,  active  in  armature,  or  electrical 

activity  of  machine. 
P"  =  mechanical  energy  at  dynamo  shaft;  /.  ^.,  driving  power 

of  generator,  output  of  motor. 
PA   =total  energy  absorbed  in  armature. 
jPM  —  total  energy  absorbed  in  field  circuits. 
P&  =  energy  absorbed  in  armature  winding  (Cltf-loss). 
P'&  =  running  value  of  armature;  /.  *.,  energy  developed  per 

unit   weight   of   copper  at  unit  speed  and  unit  field 

density. 
Pe  =  energy  absorbed  by  eddy  currents,  in  watts. 


xxxn  LIST  OF  SYMBOLS. 

P'e  —  energy  absorbed  by  eddy  currents,  in  ergs. 

Pt  =  energy  absorbed  by  brush-friction. 

Ph  =  energy  absorbed  by  hysteresis,  in  entire  armature  core. 

P'h  =  energy  absorbed  by  hysteresis,  in  solid  portion  of 
slotted  armature  core. 

P"h  —  energy  absorbed  by  hysteresis,  in  iron  projections  of 
toothed  and  perforated  armatures. 

Pk  =  energy  absorbed  by  contact  resistance  of  brushes. 

Pm  =  energy  absorbed  in  magnet  windings. 

P0  =  energy  loss  due  to  air-resistance,  brush  friction,  journal 
friction,  etc. 

P'0  =  energy  required  to  run  dynamo  at  normal  speed  on 
open  circuit. 

Pae  =:  energy  absorbed  in  series  winding. 

^sh  =  energy  absorbed  in  shunt  winding. 

P'8h  =  energy  absorbed  in  entire  shunt-circuit,  at  normal  load. 

Pr  =  energy  absorbed  in  shunt  regulating  resistance. 

P"^  =  any  load  of  a  motor,  in  watts. 

ps  =  safe  pressure,  or  working  load,  of  materials,  in  pounds 
per  square  inch. 

TC  —  ratio  of  circumference  to  diameter  of  circle,  =  3.1416. 

(R  =  reluctance  of  magnetic  circuit,  in  oersteds. 

R,  r  —  electrical  resistance,  in  ohms. 

R  —  resistance  of  external  circuit. 

RA  —  total  resistance  of  armature  wire,  all  in  series. 

ra  =  armature  resistance,  cold,  at  15.5°  Centigrade. 

r'a  =  armature  resistance,  hot,  at  (15.5  +  9a)  degrees  Cent. 

rm  =  magnet-resistance,  cold,  at  15.5°  Centigrade. 

r'm  —  magnet-resistance,  warm,  at  (15.5  +  6m)  degrees  Cent. 

rT  =  resistance  of  shunt  field  regulator. 

rse  =  resistance  of  series  winding,  cold,  at  15.5°  Centigrade. 

r'ge  —  resistance  of  series  winding,  warm,  at  (15.5  +  0m)  de- 
grees Centigrade. 

rtih  —  resistance  of  shunt  winding,  cold,  at  15.5°  Centigrade. 

r'8h  =  resistance  of  shunt  winding,  warm,  at  (15.5  -f-  em)  de- 
grees Centigrade. 

rx  =  extra-resistance,  or  shunt  regulating  resistance  in  circuit 
at  normal  load,  in  per  cent,  of  magnet  resistance. 

ri>  riii  •  •  •  —  resistances  of  coils  I,  II,  ...  of  series  field 
regulator. 


LIST  OF  SYMBOLS.  xxxill 

p±  =  resistivity  of  brush-contact,  in  ohms  per  square  inch  of 
surface. 

Pm  =  resistivity  of  magnet-wire,  in  ohms  per  foot. 

S  =  surface,  sectional  area. 

SA  =  radiating  surface  of  armature. 

S&  —  sectional  area  (corresponding  to  average  specific  mag- 
netizing force)  of  magnetic  circuit  in  armature  core. 

SAl  —  minimum  cross-section  of  armature  core. 

S&z  —  maximum  cross-section  of  armature  core. 

•So.  i.  —  sectional  area  of  magnetic  circuit  in  cast  iron  portion 
of  field  frame. 

Sc  s  =  sectional  area  of  magnetic  circuit  in  cast  steel  portion 
of  field  frame. 

St  =  actual  field  area  ;  /*.  e.,  area  occupied  by  effective 
inductors. 

Sg  =  sectional  area  of  magnetic  circuit  in  air  gaps. 

S'g  =  area  of  clearance  spaces  in  toothed  and  perforated 
armature. 

5M  =  radiating  surface  of  magnets. 

S  'M  =  surface  of  magnet-cores. 

Sm  =  sectional  area  of  magnet-frame,  consisting  of  but  one 
material. 

•Sp  =  area  of  magnet  circuit  in  polepieces  of  uniform  cross- 
section. 

vSpj  =  minimum  cross-section  of  polepieces. 

SV9  —  maximum  area  of  magnetic  circuit  in  polepieces. 

^  =:  sectional  area  of  armature  slot,  in  metric  units. 

S"s  =  sectional  area  of  armature  slot,  in  square  inches. 

•Sw.  i.  —  sectional  area  of  magnetic  circuit  in  wrought  iron  por- 
tion of  field  frame. 

Sy  =  area  of  magnetic  circuit  in  yoke. 

G  :=  factor  of  magnetic  saturation. 

7;  /  —  time. 

r  —  torque,  or  torsional  moment. 

0a  =  rise  of  temperature  in  armature,  in  degrees  Centigrade. 

6'a  =  specific  temperature  increase  in  armature,  in  degrees 
Centigrade. 

Qm  =  rise  of  temperature  in  magnets,  in  degrees  Centigrade. 

6'm  =  specific  temperature  increase  in  magnets,  in  degrees 
Centigrade. 


xxxi v  LIST  OF  SYMBOLS. 

v  —  velocity,  linear  speed. 

VB  =  belt  velocity,  in  feet  per  minute. 

v'E  =z  belt  velocity,  in  feet  per  second. 

vc  =  conductor  velocity,  or  cutting  speed,  in  feet  (or  metres) 
per  second. 

vk  ™  commutator  velocity,  in  feet  per  second. 

vm  —  velocity  of  railway  car,  in  miles  per  hour. 

M\,  wt  —  weight. 

Wt  —  total  weight  to  be  propelled  by  railway  motor,  in  tons. 

wt&  •=.  weight  of  armature  winding,  bare  wire,  in  pounds. 

wt'&  —  weight  of  armature  winding,  covered  wire. 

wtm  =  weight  of  magnet  winding,  bare  wire. 

wt'm  =  weight  of  magnet  winding,  covered  wire. 

wtse  =  weight  of  series  winding,  bare  wire. 

wt'se  —  weight  of  series  winding,  covered  wire. 

«//gll  =  weight  of  shunt  winding,  bare  wire. 

o//'sh  =  weight  of  shunt  winding,  covered  wire. 

Xa,  .xa  =  value  of  an  ordinate  corresponding  to  position,  or 
angle,  a. 

x  =  any  integer,  in  formula  for  number  of  armature  con- 
ductors. Exponent  of  size  ratio  to  give  output  ratio 
of  two  dynamos. 

Y  =  relative  hysteresis-heat  per  unit  volume  of  teeth. 
y  —  connecting-pitch,  or  spacing,  of  armature  winding;  aver- 
age pitch. 

y^  =  back- pitch;  /.  e.9  connecting-distance  on  back  of  arma- 
ture. 

yt  =2  front-pitch;  /.  <?.,  connecting  distance  on  front  of  arma 
ture  (commutator-side). 

z  =  ratio  of  speed  reduction  of  railway  motor;  /.  e.t  ratio  of 
armature  revolutions  to  those  of  car-axle. 

0  =  conductor  carrying  current  toward  observer. 

O  —  conductor  carrying  current  from  observer. 

O  —  singly  re-entrant  simplex  armature  winding. 

(§)=  doubly  re-entrant  simplex  armature  winding. 

(2)  —  triply  re-entrant  simplex  armature  winding. 

OO  —  singly  re-entrant  duplex  armature  winding. 

<5J)(5)=  doubly  re-entrant  duplex  armature  winding. 

OOO    —  singly  re-entrant  triplex  armature  winding. 
=  triply  re-entrant  triplex  armature  winding. 


PART  I. 
PHYSICAL  PRINCIPLES 

OF 

DYNAMO-ELECTRIC  MACHINES. 


DYNAMO-ELECTRIC   MACHINES: 


PART  I. 

PHYSICAL    PRINCIPLES   OF  DYNAMO-ELECTRIC 
MACHINES. 


CHAPTER    I. 

PRINCIPLES   OF    CURRENT    GENERATION    IN    ARMATURE. 

1.  Definition  of  Dynamo-Electric  Machinery. 

A  dynamo -electric  machine,  or  a  dynamo,  is  a  machine  in  which 
mechanical  energy  is  converted  into  electrical  energy,  or  vice- 
versa,  by  means  of  electromagnetic  induction. 

According  to  this  definition,  every  dynamo-electric  machine 
is  capable  of  serving  either  as  a  generator  or  as  a  motor, 
according  to  whether  it  is  supplied  with  mechanical  or  elec- 
trical energy,  and  whether  it  is,  therefore,  giving  out  electrical 
or  mechanical  energy,  respectively. 

In  an  electric  generator,  mechanical  energy  is  converted  into 
electrical  by  means  of  continuous  relative  motion  between 
electrical  conductors  and  a  magnetic  field,  or  fields,  such 
motion  causing  the  conductors  to  cut,  or  traverse,  the  lines  of 
force  of  the  field. 

In  an  electric  motor,  electrical  energy  is  transformed  into 
mechanical  by  means  of  continuously  supplying  a  system  of 
electrical  conductors  with  an  electric  current  which  causes 
a  magnetic  force  to  act  between  the  conductors  carrying  it 
and  the  magnetic  field,  or  fields,  thereby  producing  continuous 
relative  motion  between  the  conductors  and  the  magnetic 
fields. 


4  DYNAMO-ELECTRIC  MACHINES.  [§  3 

2.  Classification  of  Armatures. 

A  system  of  electrical  conductors,  arranged  for  the  purpose 
of  converting  continuous  motion  into  electrical  energy,  or  of 
electrical  energy  into  rotation,  and  attached  to  a  suitable 
^frafriey^or  structure,  is  called  the  armature  of  a  dynamo- 
e4ectric\ machine.  According  to  the  manner  of  the  arrange- 
mtrit"  ulf l  trie  rotating  conductors  the  following  kinds  of 
armatures  may  be  distinguished: 

(1)  Cylinder  or  Drum  Armatures,  in  which  the  conductors  are 
wound  longitudinally  upon  the  surface  of  a  cylinder,  or  drum; 

(2)  Ring  Armatures,    in    which   the    conductors   are   wound 
spirally  around  a  ring-shaped  core; 

(3)  Pole  or  Star  Armatures,  in  which  the  coils  are  arranged 
in  the  form  of  a  star  with  their  axes  pointing  radially; 

(4)  Disc  Armatures,    in    which    the    conductors   are    placed 
radially  upon  the  surface  of  a  disc-shaped  frame,  thus  form- 
ing flat  coils  having  their  axes  parallel  to  the  shaft; 

(5)  Smooth-Core   Armatures,    in   which    the    conductors   are 
exterior  to  the  iron  core; 

(6)  Toothed-Core   Armatures,    in   which  the   conductors   are 
imbedded  in  slots,  or  channels,  provided  upon  the  surface  of 
the  core; 

(7)  Perforated  Armatures,  in  which  the  conductors  are  drawn 
through  holes,  o.r  ducts,  extending  near  the   surface   of,   but 
entirely  within,  the  iron  body  of  the  armature  core. 

3.  Production  of  Electromotive  Force. 

When  relative  motion  takes  place  between  a  conductor  and 
a  magnetic  field,  two  kinds  of  such  movement  may  be  distin- 
guished, according  to  whether  the  conductor  does  or  does  not 
cut  across  the  lines  of  magnetic  force  of  the  field. 

If  a  conductor  A  B,  of  which  A'  B ',  Fig.  i,  is  the  plan, 
A"  B"  the  elevation,  and  A"'  B'"  an  end-view,  is  moved  either 
in  the  direction  of  the  arrows  i  or  i',  coinciding  with  its 
longitudinal  axis,  or  in  the  direction  of  the  arrows  2  or  2', 
coinciding  with  that  of  the  magnetic  lines,  or  if  its  motion  is 
composed  of  both  the  former  and  the  latter  direction,  then  it 
either  merely  passes  end-wise  through  the  field  between  two 
rows  of  magnetic  lines  parallel  to  its  axis,  or  it  slides  along 


§3] 


CURRENT   GENERATION  IN  ARMATURE. 


5 


a  row  of  lines,  or  its  motion  is  compounded  of  both  these 
movements,  passing  longitudinally  between  two  rows  of  lines 
and  in  the  same  time  sliding  along  the  lines  laterally,  respec- 
tively, but  in  none  of  these  cases  the  conductor  intersects,  or 
traverses,  the  lines  of  force  by  cutting  them  with  its  length: 
If,  however,  the  direction  of  the  motion  does  not  fall  wholly 
within  the  plane  containing  both  the  axis  of  the  conductor 
and  the  direction  of  the  lines  of  force,  for  instance  if  the 
motion  is  perpendicular  to  the  direction  of  the  magnetic  lines 
and  also  to  the  axis  of  the  conductor,  as  shown  by  arrows  3,  3', 


B"     ,./ 


Fig.  i.— Motion  of  Conductor  in  Uniform  Magnetic  Field. 

Fig.  i,  then  the  moving  conductor  cuts  the  lines  of  induction 
along  its  length  as  it  passes  through  the  field. 

In  case  the  motion  is  of  the  first  kind,  i.  e.,  if  the  conductor 
does  not  cut  across  any  lines  of  force,  no  difference  of  state  can 
be  detected  in  it  due  to  such  motion.  But  if,  in  case  of 
a  motion  of  the  second  kind,  the  conductor  does  cut  the  mag- 
netic lines,  then  a  difference  of  electric  potential  is  observed 
between  the  ends  A  and  B  during  the  motion,  that  is  to 
say,  an  electromotive  force  is  set  up  or  induced  in  the  con- 
ductor, which  therefore  more  appropriately  may  be  termed  an 
inductor,  while  it  cuts  the  lines  of  the  magnetic  field.  Due  to 
this  induced  E.  M.  F.  the  one  end  of  the  inductor  is  raised 
to  a  higher  potential  than  the  other,  in  consequence  of  which 
there  is  a  tendency  for  electricity  to  flow  along  the  inductor, 
and  if  the  two  ends  are  electrically  connected  exterior  to  the 


D  YNA MO-ELECTRIC  MA  CHINES.  [§  4 

field  so  as  to  complete  a  closed  circuit  of  conducting  material, 
as  in  Fig.  2,  this  tendency  will  be  called  into  action,  and 
a  current  will  flow. 

4.  Magnitude  of  Electromotive  Force. 

The  magnitude  of  the  E.  M.  F.  produced  in  the   conductor 
depends  upon  the  rate  at  which  the  lines  of  force  are  cut,  that 


:t: 


Fig.  2. — Moving  Conductor,  forming  Part  of  Complete  Electric  Circuit. 

is,  upon  the  total  number  of  magnetic  lines  cut  by  the  inductor 
in  a  unit  of  time.  The  number  of  lines  cut  in  any  period  of 
time  is  given  by  the  actual  field  area  swept  through  by  the 
moving  inductor  and  by  the  number  of  lines  per  unit  of  field 


<- v  — 


1-SECOND 

Fig.  3. — Moving  Conductor  in  Uniform  Magnetic  Field. 

area,  /.  e.,  by  the  density  of  the  magnetic  lines  within  that 
area;  the  rate  at  which  the  lines  are  cut,  therefore,  depends 
upon  the  length  of  the  inductor,  the  speed  of  its  motion,  the 
strength  of  the  magnetic  field,  and  upon  the  angle  between  the 
moving  conductor  and  the  direction  of  its  motion. 

If  Z,  Fig.  3.  is  the  length  of  the  inductor,  a  its  angle  with 


§  4]  CURRENT  GENERA  TION  IN  ARM  A  TURE.  7 

the  direction  of  motion,  v  its  linear  velocity  per  second,  and 
3C  the  uniform  density  of  the  lines,  then  the  total  number 
of  lines  cut  per  second,  $,  is  the  product  of  the  area  swept 
and  of  the  density,  thus  : 

<£  =  'L  X  sin  a  X  v  X  3C      ..........  (1) 

In  practical  dynamos  the  inductors  are  usually  so  arranged 
upon  the  armature  that  their  axes  are  perpendicular  to  the 
direction  of  the  motion,  /.  e.,  so  that  a  —  90°,  and  for  this 
practical  case  we  have: 

0  =  L  X  sin  90°  x  v  X  3C 

=  L  x  v  x  oe    ...................  (2) 

The  E.  M.  F.  induced  in  the  moving  inductor  is  propor- 
tional to  this  number,  hence: 

E  =  kx$  =  kxLxvxW,      .......  (3) 


where  E  —  E.  M.  F.  induced  in  moving  inductor; 
0  =  total  number  of  lines  cut  per  second; 
L  =  length  of  moving  inductor; 
v    —  linear  velocity  of  inductor  per  second; 
X  =  average  density  of  magnetic  field; 
k    —  constant,  whose  value  depends  upon  units  chosen. 

Now,  the  absolute  electric  and  magnetic  systems  of  units 
are  so  related  with  each  other  that,  if  the  number  of  magnetic 
lines  cut  per  second  is  expressed  in  C.  G.  S.  units,  the  result 
of  formula  (3)  gives  directly  the  E.  M.  F.  induced,  expressed 
in  absolute  units,  or  in  other  words,  if  an  inductor  cuts 
i  C.  G.  S.  line  per  second,  the  difference  of  potential  induced 
in  its  length  by  the  motion  causing  such  cutting,  is  i  absolute 
unit  of  E.  M.  F.  In  the  C.  G.  S.  system,  consequently,  the 
constant  k  =  i.  The  practical  unit  of  E.  M.  F.,  i  volt,  is  one 
hundred  million  times  greater  than  the  absolute  unit,  which  is 
inconveniently  small,and,  in  consequence,  100,000,000  C.  G.  S. 
lines  of  force  cut  per  second  produce  one  volt  of  E.  M.  F.  If, 
therefore,  <&  is  reckoned  in  C.  G.  S.  lines,  and  E  is  to  be 

measured,  as  usual,  in  volts,  the  value  of  the  constant  is 

i 

=  io-8, 


100,000,000 


8                              DYNAMO-ELECTRIC  MACHINES.  [£  5 

and  the  formula  for  the  E.  M.  F.,  in  practical  units,  becomes: 
£=LXvxWX  io~8  volts,      .(4) 

and  now:  L  =  length  of  inductor,  in  centimetres; 

v    =  cutting-velocity,  in  centimetres  per  second; 
3C  =  density  of  field,  in  C.  G.  S.    lines  per  square 
centimetre. 

5.  Average  Electromotive  Force. 

If  the  rate  of  cutting  lines  of  force  is  constant,  the  E.  M.  F. 
induced  at  any  instant  is  the  same  throughout  the  motion  of 


\\ 


Fig.  4. — Inductor  Describing  Circle  in  Magnetic  Field. 

the  conductor,  but  if  either  the  cutting-speed  or  the  density 
of  the  field  varies,  the  instantaneous  values  of  the  E.  M.  F. 
vary  accordingly,  and  the  average  E.  M.  F.  generated  in  the 
inductor  is  the  geometrical  mean  of  all  the  instantaneous 
values. 

In  a  dynamo  each  inductor  is  carried  in  a  circle  through  a 
more  or  less  homogeneous  field;  in  two  diametrically  opposite 
positions  therefore,  at  a  and  a',  Fig.  4,  its  motion  is  parallel 
to  the  lines  of  force,  while  at  two  positions,  b  and  b',  at  right 
angles  to  a  and  a',  the  inductor  moves  perpendicular  to  the 
lines.  In  positions  a  and  a',  consequently,  no  lines  are  cut, 
and  the  induced  E.  M.  F.  is  E  —  o,  while  at  b  and  b'  the  maxi- 
mum number  of  lines  is  cut  in  unit  time,  and  E  has  its  maxi- 
mum value.  Between  these  two  extremes  any  possible  value 
of  E  exists,  according  to  the  angular  position  of  the  inductor. 


£6]  CURRENT  GENERATION  IN  ARMATURE.  9 

The  average  value  of  the  induced  E.  M.  F.  for  any  movement 
with  a  varying  number  of  lines  cut  is  given  by  the  average  rate 
of  cutting  lines  during  that  movement,  and  the  average  rate  is 
the  quotient  of  the  total  number  of  lines  cut  divided  by  the  time 
required  to  cut  them.  The  average  E.  M.  F.,  therefore,  is 

£=  X    ICT8   VOltS,       .............  (5) 


where  E  =  average  value  of  E.  M.  F.,  in  volts; 
0  =  total  number  of  lines  of  force  cut; 
/    =  time  required  to  cut  lines,  in  seconds. 

If  the  inductor  of  Fig.  4  is  moved  with  an  angular  velocity 
of  N  revolutions  per  minute,  or  of 

N'  =  iy 

60 

revolutions  per  second,  the  number  of  lines  cut  in  the  half- 
revolution  from  a  to  a'  is  <l>,  and  the  time  taken  by  this 
half-revolution  is 


•E  =  —  X  io~8  —2    $  N'  x  io~8 


seconds;  consequently  the  average  E.  M.  F.  for  this  case  is: 

(6) 
£  xio-=.I- 

60  3 

in  which  E    =  average  value  of  E.  M.  F.,  in  volts; 
£>    =  total  number  of  lines  of  force  cut; 
N   —  cutting  speed,  in  revolutions  per  minute; 
N'  =  cutting  speed,  in  revolutions  per  second. 

6.  Direction  of  Electromotive  Force. 

The  direction  of  the  current  flowing  due  to  the  induced 
E.  M.  F.  in  any  inductor  depends  upon  the  direction  of  the 
lines  of  force  and  upon  the  direction  of  the  motion,  and  can 
be  determined  by  applying  the  well-known  "finger-rule"  of 


10 


D  YNAMO-ELECTRIC  MA  CHINES. 


Professor  Fleming.  The  directions  of  the  magnetic  lines,  of 
the  motion,  and  of  the  current  being  perpendicular  to  each 
other,  three  fingers  of  the  hand,  placed  at  right  angles  to  one 
another,  are  used  to  determine  any  one  of  these  directions 
when  the  other  two  are  known.  To  find  the  direction  of  the 
induced  E.  M.  F.  the  right  hand  is  employed,  being  placed  in 
such  a  position  that  the  t3Cumb  points  in  the  direction  of  the 
magnetic  lines  (of  density  5C),  and  the  middle  finger  in  the 
direction  of  the  /motion,  Fig.  5,  when  the/orefinger  will  indicate 


Fig.  5. — Finger  Rule  for  Direction  of 
Current.     (Right  Hand.) 


Fig.  6. — Finger  Rule  for  Direction  of 
Motion.     (Left  Hand.) 


the  direction  of  the  /low  of  the  current.  Conversely,  the 
direction  of  the  motion  which  results  if  a  conductor  carrying 
an  electric  current  is  placed  in  the  magnetic  field  of  a  magnet, 
is  obtained  by  using  in  the  same  manner  the  respective  fingers 
of  the  left  hand,  as  shown  in  Fig.  6,  and  then  the  middle  finger 
will  point  to  the  direction  in  which  the  motion  of  the  conductor 
will  take  place. 

If,  in  case  of  a  generator,  either  the  direction  of  the  lines  of 
force  or  the  direction  of  the  motion  is  reversed,  the  induced 
E.  M.  F.  will  also  be  reversed  in  direction;  and  if,  in  case  of  a 
motor,  either  the  polarity  of  the  field  or  the  direction  of  the 
current  in  the  armature  conductors  is  reversed,  the  rotation 
will  also  change  its  direction. 

In  the  armatures  of  practical  machines  the  inductors,  for  the 
purpose  of  collecting  the  E.  M.  Fs.  induced  in  each,  are  elec- 
trically connected  with  each  other,  and  thereby  a  system  of 


CURRENT  GENERATION  IN  ARMATURE. 


1 1 


armature  coils  is  formed.  According  to  the  number  of  inductors 
in  each  loop  there  are  two  kinds  of  armature  coils.  In  ring 
armatures,  Fig.  7,  each  coil  contains  but  one  inductor  per  turn, 
while  in  drum  armatures,  Fig.  8,  every  convolution  of  the  coil 
is  formed  of  two  inductors  and  two  connecting  conductors.  AT 


CONDUCTOR 


MAGNET   POLE 


Fig.  7. — Ring  Armature  Coil.  .     Fig.  8. — Drum  Armature  Coil. 

ring  armature  coil,  therefore,  when  moved  so  as  to  cut  the  lines 
of  a  magnetic  field,  has  only  one  E.  M.  F.  induced  in  it;  in  a 
drum  armature  coil,  however,  E.  M.  Fs.  are  induced  in  both  the 
inductors,  and  these  two  E.  M.  Fs.  may  be  of  the  same  or  of 
opposite  directions,  according  to  the  manner  in  -which  the  coil 


Fig.  9. — Closed  Coil  moving  Horizontally  in  Magnetic  Field. 

is  moved  with  respect  to  the  lines  of  force.  If  the  relative 
position  between  the  magnetic  axis  of  the  coil  and  the  direc- 
tion of  the  lines  does  not  change,  that  is,  if  the  angle  enclosed 
by  them  remains  the  same  during  the  entire  motion  of  the  coil, 
as  in  Fig.  9,  the  E.  M.  Fs.  induced  in  the  two  halves  counter- 


12 


DYNAMO-ELECTRIC  MACHINES. 


[§7 


act  each  other,  while  when  the  coil  is  revolved  about  an  axis 
perpendicular  to  the  direction  of  the  lines  of  force,  as  in  Figs. 
10  and  n,  the  E.  M.  Fs.  in  the  two  inductors  have  opposite 
directions,  and  therefore  add  each  other  when  flowing  around 
the  coil. 

Since  in  the  former  case,  Fig.  9,  the  number  of  lines  through 
the  coil  does  not  change,  while  in  the  latter  case,  Figs.  10  and 
n,  it  does,  it  follows  that  E.  M.  F.  is  induced  in  a  closed  circuit, 
if  this  circuit  moves  in  a  magnetic  field  so  that  the  number  of  lines  of 
force  passing  through  it  is  altered  during  the  motion.  By  applying 
the  finger-rule  to  the  single  elements  of  the  coil  it  is  found  that 


Figs.  10  and  n. — Closed  Coil  Revolving  in  Magnetic  Field. 

the  direction  of  the  induced  current  is  clockwise,  viewed  in  the 
direction  with  the  lines,  if  the  motion  is  such  as  to  cause  a 
decrease  in  the  number  of  lines;  and  is  counter-clockwise,  if  the 
motion  effects  an  increase  in  the  number  of  lines. 

7.  Collection  of  Current  from  Armature  Coil. 

If  a  coil  is  revolved  in  a  uniform  magnetic  field,  the  number 
of  lines  threading  through  it  will  twice  in  each  revolution  be 
zero,  once  a  maximum  in  one  direction,  and  once  in  the  other. 
If,  therefore,  the  current  of  that  coil  is  collected  by  means  of 
collector-rings  and  brushes,  Figs.  12  and  13,  it  will  traverse  the 
external  circuit,  from  brush  to  brush,  in  one  direction  for  one- 
half  of  a  revolution  and  in  the  opposite  direction  in  the  other 
half,  or  an  alternating  current  is  produced  by  the  coil.  In 
plotting  the  positions  of  the  coil  in  the  magnetic  field  as  ordi- 
nates  and  the  corresponding  instantaneous  values  of  the 


CURRENT  GENERA  TION  IN  ARMATURE. 


induced  E.  M.  F.  as  abscissae,  the  curve  of  induced  E.  M.  Fs., 
or,  since  the  electrical  resistance  of  the  circuit  is  constant 
during  the  motion  of  the  coil,  the  curve  of  induced  currents  is 


Figs.  12  and  13. — Collection  of  Armature  Current. 

obtained,  Fig.  14.  Since  the  instantaneous  value  e^  at  any 
moment  is  expressed  by  the  product  of  the  maximum  value 
and  the  sine  of  the  angle  through  which  the  coil  has  moved, 


o      <p     90° 


Fig.  14. — Curve  of  Induced  E.  M.  Fs. 

viz.,  e^  —  E'x  sin  cp,  the  curve  of  the  induced  E.  M.  Fs,,  in  a 
uniform  magnetic  field,  is  a  sine-wave,  or  a  sinusoid. 

8.  Rectification  of  Alternating  Currents. 

By  means  of  a  device  called  a  commutator  the  alternating 
current  delivered  by  the  coil  to  the  external  circuit  can  be 
rectified  so  as  to  flow  always  in  the  same  direction,  the  negative 
inductions  being  commutated into  positive  ones,  and  the  alternat- 
ing current  transformed  into  a  urn-directed  or  continuous  current. 

A  commutator  employed  for  this  purpose  in  continuous  cur- 
rent dynamos  consists  of  as  many  conducting  cylinder  segments 


DYNAMO-ELECTRIC  MACHINES. 


or  circle-sectors  as  there  are  coils,  in  case  of  a  ring  armature, 
and  has  twice  as  many  commutator-bars  or  -divisions  as  there 
are  coils  in  the  case  of  a  drum  armature,  each  commutator-bar 
being  insulated  from  its  neighbors,  but  in  electrical  connection 
with  the  armature  coils  and  rotating  with  them.  The  process 


> a  : + , 

Figs.  15  and  16. — Commutation  of  Armature  Current. 

of  rectification  of  the  currents  generated  in  the  drum  armature 
coil  of  Figs.  12  and  13  by  means  of  a  two-division  commutator 
is  shown  in  Figs.  15  and  16,  of  which  the  former  refers  to  the 
first  and  the  latter  to  the  second  half-revolution  of  the  coil. 
The  corresponding  curve  of  the  induced  E.  M.  Fs.  is  repre- 
sented in-  Fig.  17,  which  shows  that  the  current  issuing  from  a 


Fig.  17.—  Rectified  Curve  of  E.  M.  Fs. 

single  coil  is  of  a  pulsating  character,  its  value  periodically 
increasing  from  zero  to  a  maximum,  and  decreasing  again  to 
zero. 

9.  Fluctuations  of  Commutated  Currents. 

The  instantaneous  E.  M.  Fs.  induced  in  a  single  coil  vary- 
ing between  the  values  emin  =  o  and  ^max  =  E'  ,  the  mean 
E.  M.  F.  is 


(o 


§9] 


CURRENT  GENERATION  IN  ARMATURE. 


and  the  amount  of  fluctuation,  with  a  two-division  commuta- 
tor, is 


E' 


E' 


:  =  ±  .5,  or  ±  50$. 


In  order  to  obtain  a  less  fluctuating  current  it  is  necessary 
to  employ  more  than  one  armature  coil,  the  current  growing 


360   0 


Fig.  18. — One-Coil  Armature. 

the  steadier  the  greater  the  number  of  the  coils.  If  a  coil  of, 
say,  16  turns,  Fig.  18,  generating  a  maximum  E.  M.  P\  of 
'ma*  =  E'  volts,  is  split  up  into'two  coils  of  half  the  number 
of  turns  each,  which  are  set  at  right  angles  to  each  other, 
Fig.  19,  each  will  only  generate  half  the  maximum  E.  M.  F. 


90° 


Fig.  19. — Two-Coil  Armature. 
of  the  original  coil,  viz. : 

-  E- 

\    max  o   max  ^ 


i6 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§e 


but  each  of  them  will  have  this  maximum  value  while  the 
other  one  passes  through  the  position  of  zero  induction,  as  is 
shown  in  Fig.  20.  Hence,  if  the  E.  M.  Fs.  of  the  two  coils  are 

X 


Fig.  20. — Fluctuation  of  E.  M.  F.  in  Two-Coil  Armature. 

added  by  means  of  a  four-division  commutator,  the  minimum 
joint  E.  M.  F.  in  this  case  is 


^  m\n     


while  the  total  maximum  E.  M.  F.,  the  maximum  inductions  in 
the  two  coils  not  occurring  at  the  same  time,  does  not  reach 
the  maximum  valued"  of  the  undivided  coil,  but,  being  the 


JBSI- 


A 


Iftaf 


180 


Fig.  21.  —  E.  M.  Fs.  in  Two-Coil  Armature  at  one-eighth  Revolution. 

sum  of  the  E.  M.  Fs.  induced  at  one-eighth  revolution,  when 
both  partial  E.  M.  Fs.  are  equal,  is,  with  reference  to  Fig.  21, 


=     (',) 


.)«•   =   ~-  (Sln  45°  +  COS  45°) 


The  mean  E.  M.  F.,  therefore,  is 

(^u,  +  '~J  =  l~  (-5  +  .707")  E'  =  .60356  £', 


§9] 


CURRENT  GENERATION  IN  ARMATURE. 


and  the  fluctuation  of  the  E.  M.  F.,  with  a  four-division  com- 
mutator, amounts  to 

—  .60356)^' 


^'max  .707II..£' 

imln^Lmean  _       (-5    ~  -6o356)   E< 
^'max  .70711    E' 


or  14. 


If  each  of  the  two  coils  i  and  2,  Fig.  19,  is  again  subdivided 
into  two  coils  of  half  the  number  of  turns,  four  coils,  i',  2',  3', 


315; 


45° 


370-°- 


Fig.  22. — Four-Coil  Armature. 

and  4',  are  obtained  which  make  angles  of  45°  with  each  other, 
Fig.  22.     Plotting  the  curves  of  E.  M.  Fs.,  therefore,  we  get 

T" 


45°  90°  180°  270° 

Fig.  23.  —  Fluctuations  of  E.  M.  F.  in  Four-Coil  Armature. 


_i_^_ 


four  waves,  */,  ^',  ^s'  and  <f/,  Fig.  23,  each  varying  between  the 
values 

(ei)mm  —  (^2  )min  =   vOmin  =  (^'Jmin  =  ° 

and 

jp  i 

\^i  )max  =    (et  )max  ==   \ez  /max  ==   (^4  )mar  —    ~T"» 

4 

and  each  starting  45°  from  its  neighbor.     In  combining  each 
two  waves  90°  apart,  by  adding  their  respective  ordinates,  the 


1 8  DYNAMO-ELECTRIC  MACHINES.  [§  9 

four  waves  are  reduced  to  two,  viz.,  e"  and  *a",  the  addition  of 
which,  finally,  renders  the  resultant  curve  of  reduced  E.  M.  F., 
/",  which  fluctuates  between  the  values 


'"'min  =   (Omax  +  (',")»*  =   2    X  —  sin  45  °  +  — 

F '  7? ' 

=  —  X~V^+  —  =  (.35356  +  .25)  £'  =  .  60356  £', 

and 

'"'max  =  (ei")22%<>  +  (e*')22y2°   =  2    X   --  (sin  22^°   -f-  COS  22^°) 

.38268  -4-  .02388 

-^—  -E     :=. 65328^. 

From   this   follows   the    mean    E.    M.    F.    obtained   with   an 
eight-division   commutator: 

'"'mean  =  \  (-60356  +  .65328)  E'  =  .62842  E', 

giving  a  fluctuation  of  the  maximum  E.  M.  F.  in  the  amount  of 
(.65328  —  .62842)  E'  1 


max  -         mean 


'"'max  .65328^'  "I  ±.02486_ 

''"min  ~   ^  mean  _  (-  6o356  -.  62842)  ^  ^     f     '  .653^8 

'"'max  .65328.S'  J 

=  ±.0386,  or  3.86^. 

The  above  calculations  show  that  the  percentage  of  fluctua- 
tion rapidly  diminishes  as  the  number  of  armature  coils 
increases,  and  in  continuing  the  process  of  subdividing  the 
coils  into  sections  symmetrically  spaced  at  equal  angles,  we 
will  get  for  resultants  curves  which  more  and  more  resemble 
a  straight  line,  and  thus  indicate  the  approaching  entire  dis- 
appearance of  fluctuations  and,  therefore,  continuity  of  the 
E.  M.  F.  In  the  following  Table  I.  the  numerical  results  of 
such  continued  subdivision  of  the  armature  coils  are  given, 
the  original  maximum  E.  M.  F.  E'  being  for  convenience 
taken  as  unity: 


]  CURRENT   GENERATION  IN  ARMATURE.  19 

TABLE  I.— FLUCTUATION  OF  E.  M.  F.  OF  COMMUTATED  CURRENTS. 


NUMBER  OP 

ANGLE 

AMOUNT 

FLUCTUA- 

COMMUTA- 
TOR 

EMBRACED 

BY 

MAXIMUM 
E.  M.  F. 

MINIMUM 
E.  M.  F. 

MEAN 
E.  M.  F. 

OP 

FLUCTUA- 

TION 

IN  P.  CENT. 

DIVISIONS. 

EACH  COIL. 

TION. 

OP  MAX. 

E.  M.  FT 

2 

180° 

1. 

0. 

.5 

±.5 

±50$ 

4 

90 

.70711 

.5 

.60356 

.10356 

14.65 

8 

45 

.65328 

.60356 

.62842 

.02456 

3.86 

12 

30 

.64395 

.62201 

.63298 

.01097 

1.70 

18 

20 

.63987 

.63014 

.63500 

.00487      .76 

24 

15 

.63844 

.63298 

.63571 

.00273 

.43 

36 

10 

.63743 

.63501 

.63622 

.00121 

.19 

48 

n 

.63708 

.63571 

.636395 

.000685 

.107 

60 

6 

.63691 

.63604 

.636475 

.000435 

.068 

90 

4 

.63675 

.63637 

.63656 

.000190 

.030 

180 

2 

.63665 

.63656 

.636605 

.000045 

.007 

360 

1 

.63664 

.63660 

.63662 

.000020 

.003 

The  average  E.  M.  F.,  that  is,  the  geometrical  mean  of  all 
the  sums  of  instantaneous  E.  M.  Fs.   induced  in  the  various 


0  45U  90°  180  270°  360° 

Fig.  24. — Average  E.  M.  F.  Induced  in  Rotating  Armature. 

subdivisions  of  the  coil,  must  be  the  same  in  every  case,  for, 
the  total  number  of  turns,  the  speed,  and  the  field-strength 
remain  the  same  for  any  number  of  commutator  divisions. 


Fig.  25. — Average  E.  M.  F.  of  One-Coil  Armature. 

Numerically,  the  average  E.  M.  F.  is  the  height  of  a  rectangle 
having  an  area  equal  to  the  surface  extending  between  the 
axis  of  abscissae,  the  two  end-ordinates,  and  the  curve  of 


2O 


D  YNAMO-ELECTRIC  MA  CHINES. 


E.  M.  F.,  as  shown  in  Fig.  24.  In  case  of  the  one-coil 
armature  the  average  E.  M.  F.,  in  considering  one-half  of 
a  revolution,  is  the  height  of  a  rectangle  equal  to  the  area  of 
a  single  wave  having.fi1'  as  its  amplitude.  The  area  S  inclosed 
by  a  sinusoid  of  amplitude  E'  and  length  /,  Fig.  25,  is: 

/          f77  F' I 

S  =  -  E '       sin  X  d  X  =  •— -  (-  cos  180°  -  (-  cos  o°)) 


therefore  the  average  E.  M.  F. 

£  =  ^  =  -  X  £'  =  .63662  E1. 


(7) 


Fig.  26.— Average  E.  M.  F.  of  Two-Coil  Armature. 

For  the  two-coil  armature  the  area  Slt  Fig.  26,  of  one-quarter 
of  a  revolution  is  the  sum  of  a  rectangle  of  length 


and  height 


E' 


and  of  a  wave  of  amplitude 

-  |  (sin  45°  + cos  45°)  —  i 
and  length 


or: 


§9]  CURRENT  GENERATION  IN  ARMATURE.  21 


The  average  E.  M.  F.  in  this  case  is: 

£  =  ±  =  *-Bl<  =  2  £'  =  .  63*6,*', 


7T 


which  is  the  same  as  obtained  above  for  the  case  of  a  one-coil 
armature.  In  the  same  manner  the  average  E.  M.  F.  is 
obtained  for  any  number  of  coils  and  is  invariably  found  to  be 
.63662  of  the  maximum  E.  M.  F.  produced  if  all  of  the 
inductive  wire  is  wound  in  but  one  coil  and  connected  to  the 
external  circuit  by  a  two-division  commutator. 

As  might  be  expected  from  the  definition  of  the  average 
E.  M.  F.,  it  will  be  noted  that  the  values  of  the  mean  E.  M.  F., 
column  5,  Table  L,  for  increasing  number  of  commutator 
divisions,  approach  the  figure  .63662  for  the  average  E.  M.  F. 
as  a  limit. 


CHAPTER    II. 


THE    MAGNETIC    FIELD    OF    DYNAMO-ELECTRIC    MACHINES. 

10.  Unipolar,  Bipolar,  and  Multipolar  Induction. 

From  the  previous  chapter  it  is  evident  that  an  E.  M.  F. 
will  be  induced  in  a  conductor: 

(1)  When  the  conductor  is  moved  across  the  lines  of  force  of 
the  field  in  a  direction  perpendicular  to  its  own  axis  and  per- 
pendicular to  the  direction  of  the  lines,  Fig.  27;  and 

(2)  When  the  conductor  is  revolved  in  the  field  about  an  axis 
perpendicular  to  the  direction  of  the  lines,  Fig.  28. 

In  the  first  case,  the  inductor  aa,  Fig.  27,  as  it  cuts  the  lines 


Fig.  27. — Unipolar  Induction. 


Fig.  28. — Bipolar  Induction. 


of  the  magnetic  field  but  once  in  each  revolution  around  the 
axis  oo,  and  in  the  same  direction  each  time,  is  the  seat  of  a  uni- 
directed  or  continuous  E.  M.  F.  In  the  second  case,  however, 
the  inductor  #,  Fig.  28,  in  revolving  about  the  axis  0,  cuts  the 
lines  of  the  field  twice  in  each  revolution,  and  cuts  them  in 
the  opposite  direction  alternately;  the  inductor  #,  therefore,  is 
the  seat  of  an  alternating  E.  M.  F.  whose  direction  undergoes 
reversal  twice  every  revolution.  If  the  conductor  a  is  made  to 
rotate  in  a  multiple  field  formed  of  more  than  one  pair  of  mag- 
net poles,  Fig.  29,  it  cuts  the  lines  of  all  the  individual  fields, 
between  each  two  poles,  in  alternate  directions,  and  an 
alternating  E.  M.  F.  is  induced  in  it,  whose  direction  reverses 


11] 


THE  MAGNETIC  FIELD. 


as  many  times  in  every  revolution  as  there  are  poles  to  form 
the  multiple  field.  Since  the  induced  E.  M.  F.  in  the  first  case 
always  has  the  same  direction  along  the  length  of  the  con- 
ductor, in  the  second  case  has  two  reversals  in  every  revolu- 
tion, and  in  the  third  case  reverses  its  direction  as  many  times 
as  there  are  poles,  three  different  kinds  of  inductions  are  dis- 


Fig.  29. — Multipolar  Induction. 

tinguished  accordingly,  viz. :   Unipolar,  Bipolar,  and  Multipolar 
induction,  respectively. 

As  induction  due  to  but  one  pole  cannot  exist,  the  term  "  uni- 
polar induction,"  if  strictly  interpreted,  is  both  incorrect  and 
misleading,  and  Professor  Silvanus  P.  Thompson,  in  the  latest 
(fifth)  edition  of  his  "  Dynamo-Electric  Machinery,"  there- 
fore uses  the  word  homopolar  (homo^alike)  for  unipolar,  and 
heleropolar  (hetero  =  different)  for  bi-  and  multipolar  induction. 

11.  Unipolar  Dynamos. 

In  carrying  out  practically  the  principle  of  unipolar  induc- 
tion, as  illustrated  in  Fig.  27,  the  poles  of  the  magnet  are  made 
tubular  and  the  conductor  extended  into  the  form  of  a  disc  or 
of  a  cylinder-ring,  Figs.  30  and  31,  respectively,  in  order  to 
cause  the  unidirected  E.  M.  F.  to  be  maintained  continuously 
at  a  constant  value.  The  solid  disc  or  solid  cylinder-ring 
inductor  is  to  be  considered  as  a  number  of  contiguous  strips,  in 
electrical  contact  with  each  other,  thus  forming  a  number  of 
conductors  in  parallel  which  carry  a  correspondingly  larger 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§H 
M.  F. 


current,  but  which  do  not  increase  the  amount  of  E 
induced. 

In  order  to  increase  the  E.  M.  F.  it  would  be  necessary  to 
connect  two  or  more  conductors  in  series,  thereby  multiplying 
the  inducing  length.  But  heretofore  all  methods  which  have 
been  experimented  with  to  achieve  the  end  of  grouping  in 
series  the  conductors  on  a  unipolar  dynamo  armature  have 
failed,  for  the  reason  that  the  conductor  which  would  have  to 


Fig.  30- — Unipolar  Disc  Dynamo.  Fig.  31. — Unipolar  Cylinder  Dynamo. 

be  used  to  connect  the  two  inductors  with  each  other  will 
itself  become  an  inductor,  and,  being  joined  to  oppositely  situ- 
ated ends  of  the  two  adjoining  inductors,  will  neutralize  the 
E.  M.  F.  produced  in  a  length  of  inductor  equal  to  its  own 
length.  No  matter,  therefore,  how  many  inductors  are  placed 
"in  series"  on  the  armature,  the  resulting  E.  M.  F.  will  cor- 
respond to  the  length  of  but  one  of  them.  By  adapting  the 
ring  armature  to  this  class  of  machines,  winding  the  conductor 
alternately  backward  and  forward  across  the  field  which  is 
made  discontinuous  by  dividing  up  the  polefaces  into  separate 
projections,  loops  of  several  inductors  in  series  can  be  formed, 
round  which  the  E.  M.  F.  and  current  alternate,  the  character- 
istic feature  of  the  unipolar  continuous  current  dynamo  being 
thereby  lost,  and  unipolar  alternators  being  obtained. 

Unipolar  dynamos  being  the  only  natural  continuous  current 


§11]  THE  MAGNETIC  FIELD.  25 

machines  not  requiring  commutating  devices,  it  is  but  a  matter 
of  course  that  attempts  are  continually  being  made  to  render 
these  machines  useful  for  technical  purposes;  but  unless  the 
points  brought  out  in  the  following  are  kept  in  mind,  such 
attempts  will  be  of  no  avail.1 

From  the  fact  that  unipolar  dynamos  have  practically  but 
one  conductor,  it  is  evident  that  its  length  must  be  made 
rather  great,  and  the  whole  machine  rather  cumbersome  in 
consequence,  in  order  to  obtain  sufficient  voltage  for  commer- 
cial uses.  But  since  a  very  large  amount  of  current  may  be 
drawn  from  a  solid  disc  or  cylinder-ring,  it  follows  that  uni- 
polar dynamos  can  be  practical  machines  only  if  built  for  very 
large  current  outputs,  such  as  will  be  required  for  metallur- 
gical purposes  and  for  central  station  incandescent  lighting. 

Professor  F.  B.  Crocker  and  C.  H.  Parmly 2  have  recently 
taken  up  this  subject  in  a  paper  presented  to  the  American 
Institute  of  Electrical  Engineers,  and  have  shown  that  the 
only  practical  manner  in  which  the  unipolar  dynamo  problem 
can  be  solved,  is  by  the  use  of  large  solid  discs  or  cylinder- 
rings  of  wrought  iron  or  steel  run  at  very  high  speed  between 
the  poles  of  strong  tubular  magnets.  The  greatest  advantage 
of  such  unipolar  machines  is  their  extreme  simplicity,  tht 
armature  having  no  winding  and  no  commutator.  The  almost 
infinitesimal  armature  resistance  not  only  effects  increased 
efficiency  and  decreased  heating,  but  also  causes  the  machine 
to  regulate  more  closely  either  as  a  generator  or  as  a  motor. 
Furthermore,  there  is  no  hysteresis,  because  the  armature  and 
field  are  always  magnetized  in  exactly  the  same  direction  and 


1  See  "  Unipolar  Dynamos  which  will  Generate  No  Current,"  by  Carl  Hering, 
Electrical  World,  vol.  xxiii.  p.  53  (January  13,  1894);  A.   Randolph,  Electrical 
World,  vol.  xxiii.  p.  145  (February  3,   1894);  Bruce  Ford,  Electrical  World, 
rol.  xxiii.  p.  238  (February  24,  1894);    G.   M.  Warner,  Electrical  World,  vol. 
txiii.  p.  431  (March  31,  1894);  A.  G.  Webster,  Electrical  World,  vol.  xxiii. 
p.  491  (April  14,  1894);  Professor  Lecher,  Elektrotechn.  Zeitschr.,  January  I, 
1895,  Electrical  World,  vol.  xxv.  p.  147  (February  2,  1895);  Professor  Arnold, 
Elektrotechn.  Zeilschr.,   March    7,    1895,  Electrical  World,  vol.    xxv.  p.  427 
/April  6,  1895). 

2  "  Unipolar  Dynamos  for  Electric  Light  and  Power,"  by  F.  B.  Crocker  and 
C.  H.  Parmly,  Trans.  A.  I.  E.  E.,  vol.  xi.  p.  406  (May  16,   1894);  Electrical 
World,  vol.  xxiii.  p.  738  (June  2,  1894);  Electrical  Engineer,  vol.  xvii.  p.  468 
'May  30,  1894). 


26  D  YNA  MO- EL  E  C  TRIG  MA  CHINES.  [§12 

to  precisely  the  same  intensity.  For  similar  reasons  there  are 
no  eddy  currents,  since  the  E.  M.  F.  generated  in  any  element 
of  the  armature  is  exactly  equal  to  that  induced  in  any  other 
element,  the  magnetic  field  being  perfectly  uniform,  owing  to 
the  exactly  symmetrical  construction  of  the  magnet  frame.  The 
armature  conductor  consists  of  only  one  single  length,  conse- 
quently the  maximum  magnetizing  effect  of  the  armature  in  am- 
pere turns  is  numerically  equal  to  its  current  capacity,  and  since 
the  field  excitation  is  considerably  greater  than  this,  the  arma- 
ture reaction  cannot  be  great.  The  armature  reaction  has  the 
effect  of  distorting  and  slightly  lengthening  the  lines  of  force, 
so  that  they  do  not  pass  perpendicularly  from  one  pole  surface 
to  the  other  in  the  air  gap  and  have  a  spiral  path  in  the  iron. 
For,  the  field  current  tends  to  produce  lines  in  planes  passing 
through  the  axis,  while  the  armature  current  acts  at  right 
angles  to  the  field  current  and  produces  an  inclined  resultant. 
There  can,  of  course,  be  no  change  of  distribution  of  magnet- 
ism as  a  result  of  armature  reaction,  which  is  the  really  objec- 
tionable effect  that  it  produces  in  bipolar  and  multipolar 
machines.  Unipolar  machines  having  no  back  ampere  turns, 
an  extremely  small  air  gap,  and  but  very  little  magnetic  leak- 
age, their  exciting  power  needs  to  be  but  very  small,  compara- 
tively, and  they  have,  therefore,  a  very  economical  magnetic 
field.  Machines  of  the  type  recommended  by  Professor 
Crocker,  finally,  are  practically  indestructible,  since  they  are 
so  simple  and  can  be  made  so  strong  that  they  are  not  likely 
to  be  damaged  mechanically,  while  it  is  almost  impossible  to 
conceive  of  an  armature  being  burnt  out  or  otherwise  injured 
electrically,  as  the  engine  would  be  stalled  by  the  current 
before  it  reached  the  enormous  strength  necessary  to  fuse  the 
armature. 

Machines  possessing  all  these  important  advantages  certainly 
deserve  a  prominent  place  in  electrical  engineering,  whereas 
they  now  have  practically  no  existence  whatever. 

12.  Bipolar  Dynamos. 

While  the  homopolar  (unipolar)  dynamo  is  naturally  a  con- 
tinuous current  dynamo,  the  heteropolar  (bipolar  and  multi- 
polar)  dynamo  is  naturally  an  alternating  current  machine,  and 
has  to  be  artificially  made  to  render  continuous  currents  by 


§12] 


THE  MAGNETIC  FIELD. 


2^ 


means  of  a  commutator.  But  in  heteropolar  machines  any 
number  of  inductors  may  be  connected  in  series,  and  con- 
sequently high  E.  M.  Fs.  may  be  produced  with  comparatively 
small-sized  armatures.  In  Fig.  32  a  ring  armature  placed  in  a_ 
bipolar  field  is  shown.  The  magnetic  lines  emanating  from 
the  -A^-pole,  in  passing  over  to  the  5-pole  of  the  field  magnet, 
first  cross  the  adjacent  gap-space,  then  traverse  the  armature 
core,  and  finally  pass  across  the  gap-space  at  the  opposite 
side.  The  inductors  of  the  armature  as  they  revolve  will  cut 
these  magnetic  lines  twice  in  every  revolution,  once  each  as 


Fig.  32. — Ring  Armature  in  Bipolar  Field. 

they  pass  through  either  gap.  If  the  rule  for  the  direction  of 
the  induced  E.  M.  F. ,  as  given  in  §  6,  is  now  applied,  it  is 
found  that  in  all  the  inductors  that  descend  through  the  right- 
hand  gap-space  the  direction  of  the  induced  current  \sfrom  the 
observer,  while  in  all  inductors  that  ascend  through  the  left- 
hand  gap-space  it  is  toward  the  observer. 

If  an  armature  is  wound  as  a  ring,  the  currents  which  are 
produced  in  the  inductors  in  the  gap-space  are  added  up  by 
conductors  carrying  the  currents  through  the  inside  of  the 
ring;  when,  however,  the  armature  is  wound  as  a  drum,  the 
currents  simply  cross  at  the  ends  of  the  core  through  connect- 
ing conductors  provided  to  complete  a  closed  electric  circuit. 
In  this  manner  armature  coils  are  formed,  in  ring  as  well  as  in 
drum  armatures,  which  are  grouped  symmetrically  around  the 
armature  core.  In  order  to  yield  a  continuous  current  these 
coils  must  be  connected  at  regular  intervals  to  the  respective 
bars  of  a  commutator,  as  illustrated  by  Fig.  33.  The  currents 


28 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§12 


induced  in  the  two  gap-spaces  will  then  unite  at  the  top-bar  b, 
and  will  flow  together  in  the  upper  brush,  which,  therefore,  is 
the  positive  brush  in  this  case,  and  thence  will  return,  through 
the  external  circuit,  to  the  lower  or  negative  brush  and  will 
there  re-enter  the  armature  at  the  lowest  bar  bl  of  the  commu- 
tator, dividing  again  into  two  parts  and  flowing  through  the 
two  halves  of  the  winding  in  parallel  circuits.  The  preceding 
equally  applies  to  a  drum  winding,  but  owing  to  the  overlapping 


P'ig.  33. — Commutator  Connections  of  Bipolar  Ring  Armature. 

of  the  two  halves  of  the  windings,  the  paths  of  the  currents 
cannot  be  followed  up  as  easily  as  in  a  ring  winding. 

By  inspection  of  the  diagram,  Fig.  33,  it  is  seen  that  the 
current  after  having  divided  in  its  two  paths  goes  from  coil  to 
coil  without  flowing  down  in  any  of  the  commutator  bars,  until 
both  streams  unite  at  the  other  side  and  pass  down  into  the 
bar  of  the  commutator  which  is  at  the  time  passing  under  the 
brush.  At  the  instant  when  one  of  the  commutator  segments 
is  just  leaving  contact  with  the  brush  and  another  one  is 
coming  into  contact  with  it,  the  brush  will  rest  upon  two 
adjacent  bars  and  will  momentarily  short-circuit  one  of  the 
coils.  While  this  lasts  the  two  streams  will  unite  by  both 
flowing  into  the  same  brush  from  the  two  adjacent  com- 
mutator segments.  A  moment  later  the  short-circuited  coil 
when  it  has  passed  the  brush  will  belong  to  the  other  half  of 
the  armature,  that  is  to  say,  in  the  act  of  passing  the  brush 


§12]  THE  MAGNETIC  FIELD.  29 

every  coil  will  be  transferred  from  one  half  of  the  armature  to 
the  other,  and  will  have  its  current  reversed.  This  is,  in  fact, 
the  act  of  commutation,  and  the  conditions  under  which  it 
takes  place  govern  the  proper  functioning  of  the  machine 
when  running,  as  they  directly  control  the  presence  ami 
amount  of  sparking  at  the  brushes. 

The  production  of  sparks  is  a  consequence  of  the  property 
of  self-induction  in  virtue  of  which,  owing  to  the  current  in 
a  conductor  setting  up  a  magnetic  field  of  its  own,  it  is  im- 
possible to  instantaneously  start,  stop,  or  reverse  a  current. 
If  the  act  of  commutation  occurs  exactly  at  the  point  when 
the  short-circuited  coils  under  the  two  brushes  are  not  cutting 
any  magnetic  lines  at  all,  no  E.  M.  F.  is  induced  in  them  at 
the  time  and  they  are  perfectly  idle  when  entering  the  other 
half  of  the  armature  winding.  On  account  of  the  self- 
induction  the  current  cannot  instantly  rise  to  its  full  strength 
in  these  idle  coils,  and  it  will  spark  across  the  commutator 
bars  as  the  brushes  leave  them.  From  this  can  be  concluded 
that  the  ideal  arrangement  is  attained  if  the  brushes  are 
shifted  just  so  far  beyond  the  point  of  maximum  E.  M.  F. 
that,  while  each  successive  coil  passes  under  the  brush  and  is 
short-circuited,  it  should  actually  have  a  reverse  E.  M.  F.  of 
such  an  amount  induced  in  it  as  to  cause  a  current  of  the 
opposite  direction  to  circulate  in  it,  exactly  equal  in  strength 
to  that  which  is  flowing  in  the  other  half  of  the  armature 
which  it  is  then  ready  to  join  without  sparking.  A  magnetic 
field  of  the  proper  intensity  to  cause  the  current  in  the  short- 
circuited  coil  to  be  stopped,  reversed,  and  started  at  equal 
strength  in  the  opposite  direction  can  usually  be  found  just 
outside  the  tip  of  the  polepiece,  for  here  the  fringe  of  mag- 
netic lines  presents  a  density  which  increases  very  rapidly 
toward  the  polepiece.  Since  a  more  intense  field  is  needed 
to  reverse  a  large  current  than  is  required  for  a  small  one,  it 
follows  that  for  sparkless  commutation  the  brushes  must  be 
shifted  through  the  greater  an  angle  the  greater  the  current 
output  of  the  armature.  Since  it  takes  a  certain  length  of 
time  to  reverse  a  current,  the  brushes  must  be  of  sufficient 
thickness  to  short-circuit  the  coils  for  that  length  of  time, 
while  on  the  other  hand  they  must  not  be  so  wide  as  to  short- 
circuit  a  number  of  coils  at  the  time,  as  this  again  would 


3°  DYNAMO-ELECTRIC  MACHINES.  [§12 

increase  the  tendency  to  sparking  on  account  of  increased 
self-induction.  From  the  preceding,  then,  it  is  evident  that 
sparkless  commutation  will  be  promoted  (i)  by  dividing  up 
the  armature  into  many  sections  so  as  to  do  the  reversing  of 
the  current  in  detail ;  (2)  by  making  the  field  magnet  relatively 
powerful,  thereby  securing  between  the  pole  tips  a  fringe  of 
field  of  sufficient  strength  to  reverse  the  currents  in  the  short- 
circuited  coils;  (3)  by  so  shaping  the  pole  surfaces  as  to  give 
a  fringe  of  magnetic  field  of  suitable  extent;  (4)  by  choosing 
brushes  of  proper  thickness  and  keeping  their  contact  surfaces 
well  trimmed. 

Since  the  direction  of  a  current  causing  a  certain  motion  is 
opposite  to  the  direction  of  the  current  caused  by  that  motion, 
it  follows  that  in  a  generator  the  current  induced  in  the  short- 
circuited  coil  at  a  certain  position  has  just  the  opposite 
direction  with  relation  to  the  current  flowing  in  the  armature 
from  that  induced  in  the  short-circuited  coil  of  a  motor  in  the 
same  position,  when  rotating  in  the  same  direction.  That  is 
to  say,  if  in  a  generator  the  brushes  are  shifted  so  that  the 
current  induced  in  the  short-circuited  coil  has  the  same 
direction  as  the  current  flowing  in  the  half  of  the  armature  it 
is  about  to  join,  in  a  motor  revolving  in  the  same  direction 
and  having  its  brushes  set  in  exactly  the  same  position,  the 
current  in  the  commuted  coil,  which  absolutely  of  course  has 
the  same  direction  as  in  case  of  the  generator,  would  relatively 
have  a  direction  opposite  to  that  flowing  in  the  half  of  the 
armature  to  which  it  is  transferred  by  the  act  of  commutation. 
While  the  brushes,  in  order  to  attain  sparkless  commutation, 
must  therefore  be  shifted  with  the  direction  of  rotation,  or 
must  be  given  an  angle  of  lead  in  a  generator,  in  a  motor  they 
have  to  be  shifted  backward,  or  have  to  be  given  an  angle 
of  lag. 

In  a  generator  the  effect  of  commutation  is  a  tendency  to 
increase  the  aggregate  magnetomotive  force  and  therefore  to 
strengthen  the  field;  in  a  motor,  however,  the  effect  of  com- 
mutation is  to  decrease  the  magnetomotive  force  and  to 
weaken  the  field.  Iron  is  very  sensitive  to  slight  increases  of 
magnetomotive  force,  while  on  the  other  hand  it  is  com- 
paratively insensible  to  considerable  decrease  of  magneto- 
motive force;  in  generators,  therefore,  the  danger  of 


§12] 


THE  MAGNETIC  FIELD. 


sparking  due  to   improper   setting   of   the   brushes  is   much 
greater  than  in  motors. 

If  the  magnetic  field  is  perfectly  uniform  in  strength  all 
around  the  armature,  the  E.  M.  Fs.  generated  in  the  separate^ 
coils  will  be  all  of  equal  amount;  but  in  actual  dynamos  the 
distribution  of  the  magnetic  lines  in  the  gaps  is  always  more 
or  less  uneven,  and  the  E.  M.  Fs.  in  the  different  coils, 
therefore,  have  more  or  less  varying  strengths.  In  well- 
designed  machines,  however,  the  magnetic  lines,  although 
unevenly  distributed  around  the  armature,  are  symmetrically 


Figs.  34  and  35. — Methods  of  Exploring  Distribution  of  Potential  around 

Armature. 

situated  in  the  two  air  gaps,  and  the  total  E.  M.  F.  of  either 
half  of  the  winding,  being  the  sum  of  the  individual  E.  M.  Fs. 
of  the  separate  coils,  will  be  equal  to  the  total  E.  M.  F.  of 
the  other  half,  from  brush  to  brush.  As  the  distribution  of 
the  magnetic  flux  around  the  armature  directly  affects  the 
distribution  of  the  potential,  an  examination  of  the  latter  will 
allow  conclusions  to  be  drawn  as  to  the  former. 

There  are  two  ways  of  studying  the  distribution  of  the 
potential  around  the  armature:  (i)  by  observing  the  voltmeter- 
deflections  caused  by  the  individual  coils,  a  set  of  exploring 
brushes  being  placed,  in  turn,  against  every  two  adjacent  com- 
mutator bars,  Fig.  34,  and  (2)  by  taking  a  voltmeter-reading 
for  every  bar,  the  voltmeter  being  connected  between  one  of 
the  main  brushes  and  an  exploring  brush  sliding  upon  the 
commutator,  Fig.  35.  By  plotting  the  voltmeter  readings,  in 
the  first  case  a  curve  is  obtained  which  shows  the  relative, 


DYNAMO-ELECTRIC  MACHINES. 


[§12 


amount  of  E.  M.  F.  induced  in  each  armature  coil  when 
brought  in  the  various  parts  of  the  magnetic  field,  while  the 
curve  received  in  the  second  case  gives  the  totalized  or 
"  integrated  "  potential  around  the  armature,  such  as  is  found 
for  any  point  in  one  of  the  armature  halves  by  adding  up  the 
E.  M.  Fs.  of  all  the  coils  from  the  brush  to  that  point. 

The  investigation  of  the  distribution  of  the  potential  around 
the  commutator  is  very  useful  in  practice,  as  it  may  disclose 
unsymmetrical  distribution  of  the  magnetic  field  due  to  faulty 
design  of  the  magnet  frame,  or  to  incorrect  shape  of  the  pole- 
pieces,  or  to  other  causes.  Fig.  36  shows  the  curves  of 


0  90°  180°  270"  360 

Fig-  36. — Curves  of  Potentials  around 
Armature  at  No  Load. 


0  90°  180°  270°  3GO 

Fig.  37- — Curves  of  Potentials  around 
Armature  at  Full  Load. 


potentials  around  an  armature  rotating  in  an  evenly  dis- 
tributed field,  such  as  will  exist  in  a  well-proportioned  dynamo 
when  there  is  no  current  flowing  in  the  armature,  that  is  to 
say,  w-hen  the  machine  is  running  on  open  circuit.  In  Fig.  37 
similar  curves  are  given  for  a  correctly  designed  dynamo  with 
unevenly  but  symmetrically  distributed  field,  as  distorted  by 
the  action  of  the  armature  current  when  running  on  closed 
circuit.  In  both  diagrams  A  is  the  curve  of  potentials  in  each 
coil,  obtained  by  the  first  method,  and  B  the  curve  of  inte- 
grated potential,  obtained  by  the  second  method  of  exploring 
the  distribution  of  potential  around  the  commutator. 

If  either  one  of  the  curves  A  or  B  is  given  by  experiment, 
the  ordinates  of  the  other  may  be  directly  obtained  by  one 
of  the  following  formulae  given  by  George  P.  Huhn:1 


1  "  On  Distribution  of  Potential,"  by  George  P.  Huhn,  Electrical  Engineer, 
vol.  xv.  p.  1 86  (February  15,  1893). 


§13] 


and 


•**-a     — 


THE  MAGNETIC  FIELD. 
i  —  cos  a 


33 


X 


sm  a 


X 


2H , 


,,  sin  a  TC 

—    Xa       X     rTtrrf  -     X 

i  —  cos  a          2  n 


in  which  Xa  =  ordinate,  at  angle  a  from  starting  position  of 

curve  of  integral  potential; 
xa  —  ordinate,  at  angle  a  from  starting  position  of 

curve  of  potential  in  each  coil; 
nc  =  number  of  commutator  divisions. 

The  potentials  may  also  with  advantage  be  plotted  out  round 
a  circle  corresponding  to  the  circumference  of  the  commutator, 
the  reading  for  each  coil  being  projected  radially  from  the 


Fig.  38.— Distribu- 
tion of  Potential 
around  Commu- 
tator at  No  Load. 


.  39- — Distribution 
of  Potential  around 
Commutator  at  Full 
Load. 


Fig.  40. — Distribution 
of  Potential  around 
Commutator  of  Faulty 
Dynamo. 


respective  commutator  division.  Fig.  38  shows,  thus  plotted, 
the  curve  of  potentials  at  no  load,  and  Fig.  39  that  at  full  load 
of  a  well-arranged  dynamo,  while  Fig.  40  depicts  the  distribu- 
tion of  potential  around  the  commutator  of  a  badly  designed 
machine. 

13.  Multipolar  Dynamos. 

While  bipolar  dynamos  offer  advantages  when  small  capaci- 
ties are  required,  their  output  per  unit  of  weight  does  not 
materially  increase  with  increasing  size,  and  a  more  economical 
form  of  machine  is  therefore  desired  for  large  outputs.  In 
order  that  the  weight-efficiency  (output  per  pound  of  weight)  of 
a  dynamo  may  be  increased  without  increasing  the  periphery 
velocity  of  the  armature,  or  dangerously  increasing  the  tern- 


34  DYNAMO-ELECTRIC  MACHINES.  [§13 

perature  limit,  it  is  necessary  to  decrease  the  reluctance  of  the 
magnetic  circuit,  that  is,  to  reduce  the  ratio  of  the  length  of 
the  air  gap  to  the  area  of  its  cross  section.  Since  the  length 
of  the  armature  cannot  be  increased  beyond  certain  limits 
governed  by  mechanical  as  well  as  magnetical  conditions,  the 
only  means  of  increasing  the  gap  area  remains  to  increase  the 
armature  diameter.  Increasing  the  diameter  of  an  armature 
allows  a  greater  circumference  on  which  to  wind  conductors, 
and  therefore  the  depth  of  the  winding  may  be  proportionally 
decreased.  Thus  the  increase  of  the  armature  diameter  not 
only  increases  the  gap  area,  but  also  decreases  its  length,  and 
consequently  very  effectively  reduces  the  reluctance  of  the 
magnetic  circuit.  With  armatures  of  such  large  diameters,  in 
order  to  more  evenly  distribute  the  magnetic  flux,  and  to  more 
economically  make  use  of  space  and  weight  of  the  magnet 
frame,  it  is  advantageous  to  divide  the  magnetic  circuit, 
resulting  in  dynamos  with  more  than  one  pair  of  poles,  or  multi- 
folar  dynamos. 

For  small  multipolar  dynamos  drum  armatures  are  often  used ; 
large  machines  for  continuous  current  work,  however,  have 
always  ring  armatures.  In  a  multipolar  armature  there  are  as 
many  neutral  and  commutating  planes  as  there  are  pairs  of  poles, 
and,  therefore,  as  many  sets  of  brushes  as  there  are  poles. 
Often,  however,  all  commutator  segments  that  are  symmetri- 
cally situated  with  respect  to  the  separate  magnetic  circuits 
are  cross-connected  among  each  other,  so  that  the  separate 
portions  of  the  armature  winding  corresponding  to  the  separate 
magnetic  circuits  are  actually  connected  in  parallel  within  the 
machine,  and  then  only  two  brushes,  in  any  two  subsequent 
planes  of  commutation,  are  necessary.  But  unless  the  arma- 
ture is  in  excellent  electric  and  magnetic  balance,  and  all  the 
magnetic  circuits  of  the  machine  have  an  equal  effect  on  the 
armature,  excessive  heating  and  sparking  are  bound  to  result 
from  this  arrangement.  This  trouble  may  be  avoided  by  wind- 
ing the  armature  so  that  the  current  is  divided  between  only 
two  paths,  exactly  as  in  a  bipolar  machine.  When  such 
a  two-path,  or  series,  winding  is  used,  the  wire  of  each  coil  must 
cross  the  face  of  the  core  as  many  times  as  there  are  field- 
poles,  the  turns  being  spaced  at  a  distance  equal  to  nearly  the 
pitch  of  the  poles.  Series-wound  multipolar  armatures  will 


§14]  THE  MAGNETIC  FIELD.  35 

operate  satisfactorily  regardless  of  inequalities  in  the  strength 
of  the  magnetic  circuits.  Unless  specially  arranged,  these 
armatures  require  only  two  brushes  which  are  180°  apart  in 
machines  having  an  odd  number  of  pairs  of  poles,  and  at  a_n 
angular  distance  apart  equal  to  the  pitch  of  the  poles  in 
machines  having  an  even  number  of  pairs  of  poles. 

Sometimes  the  commutators  of  series  armatures  are  arranged 
with  twice  as  many  bars  as  there  are  coils  in  the  armature,  in 
which  case  the  extra  bars  are  properly  cross-connected  to  the 
active  bars,  so  that  four  brushes  may  be  used  in  order  to  give 
a  greater  current-carrying  capacity.  To  economize  wire  in 
multipolar  armatures,  it  is  of  advantage  to  arrange  the  winding 
so  that  no  wires  have  to  pass  through  the  inside  of  the  ring, . 
the  inductors  being  connected  by  conductors  on  either  face  of 
the  core.  An  armature  so  wound  is  termed  a  drum-wound  ring 
armature. 

If  the  dynamos  are  to  be  directly  coupled  to  the  steam 
engines,  particularly  low  rotative  speeds  of  the  armatures  are 
required,  and  their  diameters  are  then  made  extra  large  in 
order  to  give  them  low  speed  without  too  great  a  reduction  of 
periphery  velocity.  To  fully  utilize  the  large  armature  circum- 
ference of  such  low  speed  multipolar  machines,  the  number  of 
poles  is  usually  made  very  high,  their  actual  number  depending 
upon  the  capacity  of  the  machine  and  the  service  required  of 
it.  Great  reductions  of  rotative  speed  can,  however,  only  be 
obtained  either  by  considerable  sacrifice  of  weight-efficiency,  or 
by  sacrificing  sparkless  operation.  The  former,  when  carried 
to  an  extreme,  makes  too  expensive  a  machine,  and  the  latter 
causes  increased  repairs  and  depreciation;  a  mean  between  the 
two  must  therefore  be  followed  in  practice. 

14.  Methods  of  Exciting  Field  Magnetism. 

In  modern  dynamos  the  field  magnetism  is  excited  by  current 
from  the  armature  of  the  machine  itself.  According  to  the 
manner  in  which  current  is  taken  from  the  armature  and  sent 
through  the  field  winding,  we  distinguish,  as  far  as  continuous 
current  machines  are  concerned,  the  following  classes  of 
dynamos:  (a)  Series-wound,  or  Series  dynamo;  (ti)  Shunt- 
wound,  or  Shunt  dynamo,  and  (c)  Compound-wound,  or  Com- 
pound dynamo. 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§14 


a.    Series  Dynamo. 

In  the  series-wound  dynamo  the  whole  current  from  the 
armature  is  carried  through  the  field-magnet  coils,  the  latter 
being  wound  with  comparatively  few  turns  of  heavy  copper 


Fig.  41. — Diagram  of  Series- Wound  Dynamo. 

wire,  cable,  or  ribbon,  and  connected  in  series  with  the  main 
circuit,  Fig.  41. 
Denoting  by 

E  —  total  E.  M.  F.  generated  in  armature; 

/'  =  total  current  generated  in  armature; 

r&  =  armature  resistance; 

E  —  terminal  voltage,  or  potential  of  dynamo; 

/   =  useful  current  flowing  in  external  circuit; 

R  —  resistance  of  external  or  working  circuit; 

Im  =  current  in  series  field; 

rse  =  resistance  of  series-field  coil; 

7;e  =  electrical  efficiency; 

the  following  equations  exist,  by  virtue  of  Ohm's  law  of  the 
electric  circuit,  for  the  series  dynamo: 

E' 


(8) 


=  I-.-.r 


§14]  THE  MAGNETIC  FIELD.  37 


=  E 


useful  energy 
^e  "  "    total  energy 

-  /2-# 

/"'  2  /  >P     i 
./      ( -/t  — j—  T 

From  equations  (8)  it  is  evident  that  an  increase  in  the 
working  resistance  directly  diminishes  the  current  in  the  field 
coils,  therefore  reducing  the  amount  of  the  effective  magnetic 
flux,  and  that  on  the  other  hand  a  decrease  of  the  external 
resistance  tends  to  increase  the  excitation  and,  in  consequence, 
the  flux.  The  constancy  of  the  flux  thus  depending  upon  the 
constancy  of  the  current  strength  in  series-wound  dynamos, 
these  machines  are  best  adapted  for  service  requiring  a  con- 
stant current,  such  as  series  arc  lighting. 

Equation  (9)  shows  that  the  current  generated  in  the  arma- 
ture of  a  series  dynamo,  in  order  to  overcome  the  resistances 
of  armature  and  series  field,  loses  a  portion  of  its  E.  M.  F. ; 
the  E.  M.  F.  to  be  generated  in  the  armature  of  a  series-wound 
machine,  therefore,  is  equal  to  the  required  useful  potential, 
increased  by  the  drops  in  the  armature  and  in  the  series-field 
winding.  Series  machines  having  but  one  circuit  the  current 
intensity  is  the  same  throughout,  and  consequently  the  current 
to  be  generated  in  the  armature  is  equal  to  the  current  required 
in  the  external  circuit. 

The  end  result  of  equation  (10)  shows  that  the  electrical 
efficiency  of  a  series  dynamo  is  obviously  a  maximum  when  the 
armature  resistance  and  field  resistance  are  both  as  small  as 
possible.  In  practice  they  are  usually  about  equal. 

The  series-wound  dynamo  has  the  disadvantage  of  not  start- 
ing action  until  a  certain  speed  has  been  attained,  or  unless  the 
resistance  of  the  circuit  is  below  a  certain  limit,  the  machine 
refusing  to  excite  when  there  is  too  much  resistance  or  too 
little  speed. 

b.    Shunt  Dynamo. 

In  the  shunt-wound  dynamo  the  field-magnet  coils  are 
wound  with  many  turns  of  fine  wire,  and  are  connected  to  the 
brushes  of  the  machine,  constituting  a  by-pass  circuit  of  high 


D  YNA MO-  ELE C  TRIG  MA  CHINES. 


resistance  through  which  only  a  small  portion  of  the  armature 
current  passes,  Fig.  42. 

Using  similar  symbols  as  in  the  case  of  the  series  dynamo, 


Fig.  42. — Diagram  of  Shunt-Wound  Dynamo. 

the  following  fundamental  equations   for   the  shunt  dynamo 
can  be  derived: 

/•  =  /  +  /*  =  /+£ 

^Sh 


R 


I    -     E  • 

~' 


£'  = 


,..(11) 


> (12) 


El 


& 


+  -£  +  2-a-  +  — H1 


si. 


§  14]  THE   MAGNETIC  FIELD.  39 

Equations  (n)  show  that  in  a  shunt  dynamo  an  increase  of 
the  external  resistance,  by  diminishing  the  current  in  the 
working  circuit,  increases  the  shunt  current,  and  with  it  the 
magnetic  flux,  while  a  decrease  of  the  working  resistance 
increases  the  useful  current,  the  sum  of  which  and  the  shunt 
current  is  a  constant  as  long  as  the  total  current  generated  in 
the  armature  remains  the  same,  thereby  reducing  the  exciting 
current  and  ultimately  decreasing  the  magnetic  flux.  The  flux 
remains  constant  only  when  the  potential  of  the  machine  is 
kept  the  same,  as  then  the  shunt  current,  which  is  the  quotient 
of  the  terminal  pressure  and  the  constant  shunt  resistance,  is 
also  constant;  shunt-wound  machines,  therefore,  are  best 
adapted  for  service  demanding  a  constant  supply  of  pressure, 
such  as  parallel  incandescent  lighting. 

Since  the  stronger  a  current  flows  through  the  shunt  circuit 
the  less  is  the  current  intensity  of  the  main  circuit,  a  shunt 
machine  will  refuse  to  excite  itself  if  the  resistance  of  the  main 
circuit  is  too  low. 

From  (n)  and  (12)  it  is  seen  that  the  armature  current  of  a 
shunt  dynamo  suffers  a  loss  both  in  E.  M.  F.  and  in  intensity 
within  the  machine;  E.  M.  F.  being  lost  in  overcoming  the 
armature  resistance,  and  current  intensity  in  supplying  the 
shunt  circuit.  In  consequence,  the  E.  M.  F.  to  be  generated 
in  a  shunt  dynamo  must  be  equal  to  the  potential  required  in 
the  working  circuit,  plus  the  drop  in  the  armature;  and  the 
total  current  is  equal  to  the  useful  amperage  required,  plus 
the  current  strength  used  for  field  excitation. 

The  efficiency  of  a  shunt  dynamo,  by  equation  (13),  becomes 
maximum  under  the  condition  *  that 


Inserting  this  value  in  (13)  we  obtain  the  equation  for  the  max- 
imum electrical  efficiency  of  a  shunt  dynamo: 


1  Sir  W.  Thomson  (Lord  Kelvin),  La  Lumiire  Electr.,  iv.,  p.  385  (1881). 


40  DYNAMO-ELECTRIC  MACHINES.  [§14 

Now,  since  the  armature  resistance  is  usually  very  small  com- 
pared with  the  shunt-field  resistance,  the  sum  r&  -\-  rBh  may  be 
replaced  by  rsh,  and  the  quotient 


sh 


may  be  neglected,  when  the  following  very  simple  approximate 
value  of  the  efficiency  is  obtained: 

(16) 


1  +  2 

and  this,  by  transformation,  furnishes 


By  means  of  equation  (16)  the  approximate  electrical  efficiency 
of  any  shunt  dynamo  can  be  computed  if  armature  and  magnet 
resistance  are  known;  and  from  formula  (17)  the  ratio  of 
shunt  resistance  to  armature  resistance  for  any  given  per- 
centage of  efficiency  can  directly  be  calculated.  In  the  follow- 
ing Table  II.  these  ratios  are  given  for  electrical  efficiencies 
from  7/e  =  .8,  to  7/e  =  .995,  or  from  80  to  99.5  per  cent.  : 

TABLE  II. — RATIO  OF  SHUNT  TO  ARMATURE  RESISTANCE  FOR 
DIFFERENT  EFFICIENCIES. 


PERCENTAGE  OF 
ELECTRICAL 
EFFICIENCY. 

RATIO  OF  SHUNT 
TO  ARMATURE 
RESISTANCE. 

PERCENTAGE  OF 
ELECTRICAL 
EFFICIENCY. 

RATIO  OF  SHUNT 
TO  ARMATURE 

RESISTANCE. 

100  r;e 

ra 

100  r,e 

rsh 
ra 

80$ 

64 

95.5$ 

1,802 

85 

128 

96 

2,304 

87.5 

196 

96.5 

3,041 

90 

324 

97 

4,182 

91 

409 

97.5 

6,084 

92 

529 

98 

9,604 

93 

706 

98.5 

17,248 

94 

982 

99 

39,204 

95 

1,444 

99.5 

158,404 

§14] 


THE  MAGNETIC  FIELD. 


c.  Compound  Dynamo. 

Compound  winding  is  a  combination  of  shunt  and  series 
excitation.  The  field  coils  of  a  compound  dynamo  are  partly 
wound  with  fine  wire  and  partly  with  heavy  conductors,  the__ 
fine  winding  being  traversed  by  a  shunt  current  and  the  heavy 
winding  by  the  main  current.  The  shunt  circuit  may  be 
derived  from  the  brushes  of  the  machine  or  from  the  terminals 
of  the  external  circuit;  in  the  former  case  the  combination  is 
termed  a  short  shunt  compound  winding,  or  an  ordinary  compound 
winding,  Fig.  43,  in  the  latter  case  a  long  shunt  compound  wind- 
ing, Fig.  44. 

Employing  the  same  symbols  as  before,  the  application  of 


L JL_L-R / 

Fig-  43- — Diagram  of  Ordinary  Compound- Wound  Dynamo. 


Ohm's  law  furnishes  the  following  equations  for  the  compound 
dynamo: 

(i)  Ordinary  Compound  Dynamo  (Fig.  43). 


78h  =  7se  +  7, 


sh 


/sh  =  —  =    -  —  --*  =  J  X  Ss-?1 — 


Sh 


>  ....(18) 


42 


DYNAMO-ELECTRIC  MACHINES. 


[§14 


El 


r  R 


ET  -  r  va 


(2)  Z<?«^  Shunt  Compound  Dynamo  (Fig.  44). 


....(19) 


>...(20) 


L E_J__R J 

Fig.  44. — Diagram  of  Long  Shunt  Compound- Wound  Dynamo. 


E         _        R 
-  —  I  X  — 


(21) 


£'  =  E  +  I'  (r. 


+ 


(22) 


§14]  THE  MAGNETIC  FIELD.  43 

r  R 


1  +  r*  t r*e  + 2  ra .+  rse  +  —  ^±_^-e-± 


sh 


(23)- 


By  combining  the  shunt  and  series  windings,  the  excitation 
of  the  dynamo  can  be  held  constant,  as  the  main  current 
diminishes  and  the  shunt  current  increases  with  increasing 
working  resistance,  and  the  main  current  rises  and  the  shunt 
current  decreases  with  decreasing  external  resistance.  A 
compound-wound  dynamo,  therefore,  if  properly  proportioned, 
will  maintain  a  constant  potential  for  varying  load.  In  the 
case  of  the  ordinary  compound  dynamo,  the  potential  between 
the  brushes  is  thus  kept  constant,  in  case  of  the  long  shunt 
compound  dynamo  the  potential  between  the  terminals  of  the 
working  circuit.  Although,  therefore,  the  latter  arrangement 
is  the  more  desirable  in  practice,  in  a  well-designed  dynamo  it 
makes  very  little  difference  whether  the  shunt  is  connected 
across  the  brushes  or  across  the  terminals  of  the  external 
circuit. 

In  the  ordinary  compound  dynamo  the  series  winding  sup- 
plies the  excitation  necessary  to  produce  a  potential  equal  in 
amount  to  the  voltage  lost  by  armature  resistance  and  by  arma- 
ture reaction;  in  the  long  shunt  compound  dynamo  the  series 
winding  compensates  for  armature  reaction,  and  for  the  drop  in 
the  series  field  as  well  as  for  that  in  the  armature.  The  series 
winding  may  even  be  so  proportioned  that  the  increase  of 
pressure  due  to  it  exceeds  the  lost  voltage,  and  then  the 
dynamo  is  said  to  be  over -compounded,  and  gives  higher  voltage 
at  full  load  than  on  open  circuit.  Compound  dynamos  used 
for  incandescent  lighting  are  usually  about  5  per  cent,  over- 
compounded  in  order  to  compensate  for  drop  in  the  line  from 
the  machine  to  the  lamps. 

The  armature  current  of  a  compound  dynamo  suffering  a  drop 
both  in  potential  and  in  intensity  within  the  machine,  in  calcu- 


44  DYNAMO-ELECTRIC  MACHINES.  [§14 

lating  a  compound-wound  machine  the  total  E.  M.  F.  to  be 
generated  must  be  taken  equal  to  the  required  potential  plus 
the  voltage  necessary  to  overcome  armature  and  series-field 
resistances;  and  the  total  current  strength  of  the  armature 
equal  to  the  intensity  of  the  external  circuit  increased  by  the 
current  used  in  exciting  the  shunt  field. 


PART  II. 
CALCULATION  OF  ARMATURE. 


CHAPTER  III. 

FUNDAMENTAL    CALCULATIONS    FOR    ARMATURE    WINDING. 

15.    Unit  Armature  Induction. 

It  is  evident  that  a  certain  length  of  wire  moving  with  the 
same  speed  in  magnetic  fields  of  equal  strengths  will  invariably 
generate  the  same  electromotive  force,  no  matter  whether  the 
said  length  of  wire  be  placed  on  the  circumference  of  a  drum 
or  of  a  ring  armature,  and  no  matter  whatever  may  be  the 
shape  of  the  field  magnet  frame,  or  the  number  of  poles  of  the 
different  magnetic  fields. 

In  order  to  obtain  such  a  constant,  suitable  for  practical 
purposes,  we  start  from  the  definition:  "  One  volt  E.  M.  F.  is 
generated  by  a  conductor  when  cutting  a  magnetic  field  at  the  rate  of 
100,000,000  C.  G.  S.  lines  of  force  per  second." 

Since  the  English  system  of  measurement  is  still  the  standard 
in  this  country,  we  will  take  one  foot  as  the  unit  length  of  wire, 
and  one  foot  per  second  as  its  unit  linear  velocity,  and  for  the 
unit  of  field  strength  we  take  an  intensity  of  one  line  of  force 
per  square  inch.  At  the  same  time,  however,  for  calculation  in 
the  metric  system,  one  metre  is  taken  as  the  unit  for  the  length 
of  the  conductor,  one  metre  per  second  as  the  unit  velocity,  and 
one  line  per  square  centimetre  as  the  unit  of  field  density. 

Based  upon  the  law:  "The  E.  M.  F.  generated  in  a  con- 
ductor is  directly  proportional  to  the  length  and  the  cutting 
speed  of  the  conductor,  and  to  the  number  of  lines  of  force 
cut  per  unit  of  time,"  we  can  then  derive  the  unit  amounts 
of  E.  M.  F.  generated  in  the  respective  systems  of  measure- 
ment, with  the  following  results: 

"  Every  foot  of  inductor  moving  with  the  velocity  of  one  foot  per 
second  in  a  magnetic  field  of  the  density  of  one  line  of  force  per 
square  inch  generates  an  electromotive  force  of  144  X  io~*  volt" 
and  "  Every  metre  of  inductor  cutting  at  a  speed  of  one  metre  per 
second  through  a  field  having  a  density  of  one  line  per  square  centi- 
metre generates  io~*  volt." 

47 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§15 


The  derivation  of  these  two  laws  from  the  fundamental  defi- 
nition is  given  in  the  following  Table  III. : 

TABLE  III.— UNIT  INDUCTIONS. 


LENGTH  OP 
INDUCTOR. 

CUTTING 
VELOCITY. 

DENSITY  OF  FIELD. 

E.  M.  F. 
GENERATED. 

1  foot 
1  foot 
1  foot 

1  ft.  per  second 
1  ft.  per  second 
1  ft.  per  second 

100,000,000  lines  per  sq.  ft. 
100,000,000  lines  per  sq.  in. 
1  line  per  sq.  in. 

1  Volt 
144  Volts 
144X10-8  Volt 

1  cm. 

1  metre 
1  metre 
1  metre 

1  cm.  per  second 
1  m.  per  second 
1  m.  per  second 
1  m.  per  second 

100,000,000  lines  per  sq.  cm. 
100,000,000  lines  per  sq.  m. 
100,000,000  lines  persq.  cm. 
1  line  per  sq.  cm. 

1  Volt 
1  Volt 
10,000  Volts 
10-*  Volt 

If  two  or  more  equal  lengths  are  connected  in  parallel,  in 
each  of  these  wires  every  unit  of  length  will  produce  the  respec- 
tive unit  of  induction,  but  these  parallel  E.  M.  Fs.  will  not  add, 
but  the  total  E.  M.  F.  generated  in  one  length  will  also  be 
the  total  E.  M.  F.  output  of  the  combination. 

In  an  ordinary  bipolar  armature,  now,  there  are  two  such 
parallel  branches,  each  branch  generating  the  total  E.  M.  F. 
This  necessitates  one  foot  of  generating  wire  in  each  of  these 
two  parallel  circuits,  or  altogether  two  feet  of  wire,  under  our 
unit  conditions,  in  order  to  obtain  an  E.  M.  F.  output  of 
144  x  io~8  volt;  or,  in  other  words:  Every  foot  of  the  total  gen- 
erating wire  on  a  bipolar  armature,  at  a  cutting  speed  of  one  foot 
per  second,  in  a  field  of  one  line  per  square  inch,  generates  72  X  io~* 
volt  of  the  output  E.  M.  F.  And  by  a  similar  consideration  we 
find  for  the  metric  system:  Every  metre  of  the  actual  inductive 
wire  on  a  bipolar  armature  revolving  with  a  cutting  velocity  of  one 
metre  per  second  in  a  field  of  one  line  per  square  centimetre,  gen- 
erates 5  X  io~b  volt  of  the  output  E.  M.  F. 

In  multipolar  armatures  the  number  of  the  electrically  paral- 
lel portions  of  the  winding  generally  is  2;z'p,  the  number  of 
pairs  of  parallel  armature  circuits,  or  the  number  of  bifurca- 
tions of  the  current  in  the  armature  being  denoted  by  #'p,  and 
usually  2«'p  is  equal  to  the  number  of  poles,  2«p,  the  number 
of  pairs  of  poles  being  denoted  by  «p.  In  such  armatures  it 
therefore  takes  2«'p  feet  of  generating  conductor  to  produce 
144  x  io~8  volt  of  output,  or  the  share  of  E.  M.  F.  contrib- 


§15]  FUNDAMENTAL   CALCULATIONS  FOR    WINDING.        49 

uted  to  the  total  output  by  every  foot  of  the  generating  wire 
on  the  entire  pole-facing  circumference  is 


144  x  io~8          72  X 


volt  ;  that  is,  72  X  io~*  volt  per  pair  of  armature  circuits,  or 
per  pair  of  poles,  respectively.  In  metric  units  the  share  of 
the  E.  M.  F.  contributed  to  the  output  of  a  multipolar  arma- 
ture by  every  metre  of  the  inductive  length  of  the  armature 
conductor  is 

5  X  io~5 


volt,  or  5  X  fO~b  volt  per  bifurcation. 

These  theoretical  values  of  the  "  unit  armature  induction" 
however,  have  to  undergo  a  slight  modification  for  prac- 
tical use,  owing  to  the  fact  that  generally  only  a  portion  of  the 
total  generating  or  active  wire  of  an  armature  is  effective. 
"Active"  is  all  the  wire  that  is  placed  upon  the  pole-facing 
surface  of  the  armature,  "  effective"  only  that  portion  of  it 
which  is  actually  generating  E.  M.  F.  at  any  time;  that  is,  the 
portion  immediately  opposite  the  poles  and  within  the  reach  of 
the  lines  of  force,  at  that  time. 

The  percentage  of  effective  polar  arc,  in  modern  dynamos, 
according  to  the  number  and  arrangement  of  the  poles,  varies 
from  50  to  100  per  cent,  and,  usually,  lies  between  70  and  80 
per  cent.,  corresponding  to  a  pole  angle  of  120°  to  144°, 
respectively.  The  lowest  values  of  the  effective  arc,  50  to  60 
per  cent,  of  the  total  circumference,  are  found  in  the  multipo- 
lar machines  made  by  Shuckert,  with  poles  parallel  to  the 
armature  shaft,  and  having  no  separate  pole  shoes;  in  these 
the  space  taken  up  by  the  magnet  winding  prevents  the  poles 
from  being  as  close  together  as  in  machines  of  other  types. 
The  highest  figure,  100  per  cent.,  is  met  in  some  of  the  "  All- 
gemeine  Elektricitaets  Gesellschaft"  dynamos,  in  which  the 
poles  are  united  by  a  common  cast-iron  ring  (Dobrowolsky's 
pole  bushing.  See  §  76,  Chap.  XV.). 

In  fixing  a  preliminary  value  of  this  percentage,  ftlt  in  case 
of  a  new  design,  take  67  to  80  per  cent.,  or  (3^  =  .67  to  .80,  for 
smooth  drum  armatures;  /?t  =  .75  to  .85  for  smooth  rings,  and 


D  YNA  MO-ELE  C  TRIG  MA  CHINES. 


[§16 


/?!  =  .70  to  .90  for  toothed  and  perforated  armatures.  The 
lower  of  the  given  limits  refers  to  small,  and  the  upper  to  large 
sizes,  for  the  final  value  of  ftl  is  determined  with  reference  to 
the  length  of  the  air  gaps,  and  the  latter  are  comparatively 
much  smaller  in  large  than  in  small  dynamos.  Also  the  num- 
ber of  the  magnet  poles  somewhat  affects  the  selection  of  /?„ 
the  smaller  a  percentage  usually  being  preferable  the  larger 
the  number  of  field  poles. 

For  these  various  percentages  the  author  has  found  the 
average  values  of  the  unit  armature  induction  given  in  the 
following  Table  IV. : 

TABLE  IV.— PRACTICAL  VALUES  OF  UNIT  ARMATURE  INDUCTION. 


E.  M.  F.  PER  PAIR  OF  ARMATURE  CIRCUITS. 

PERCENTAGE 

ENGLISH  UNITS. 

METRIC  UNITS. 

OF 

Volt  per  Foot. 

Volt  per  Metre. 

POLAR  ARC. 

BIPOLAR 

MULTIPOLAR 

BIPOLAR 

MULTIPOLAR 

DYNAMOS. 

DYNAMOS. 

DYNAMOS. 

DYNAMOS. 

ft 

e 

e 

ei 

ei 

1.00 

72  X  10-8 

72  X  10-8 

5     X  10-5 

5      X  10-' 

.95 

71 

68 

4.9 

4.8 

.90 

70 

65 

4.8 

4.6 

.85 

67.5 

62.5 

4.7 

4.4 

.80 

65 

60 

4.6 

4.2 

.75 

62.5 

57.5 

4.4 

4 

.70 

60 

55 

4.2 

3.8 

.65 

57.5 

52.5 

4 

3.6 

.60 

55 

50 

3.8 

3.4 

.55 

52.5 

47.5 

3.6 

3.2 

.50 

50 

45 

3.4 

3 

It  will  be  noticed  that  the  values  for  multipolar  machines 
run  somewhat  below  those  for  bipolar  ones.  This  means  that, 
at  the  same  rate  of  polar  embrace,  a  greater  percentage  of  the 
total  active  wire  is  effective  in  the  case  of  a  bipolar  machine, 
which  is  undoubtedly  due  to  a  greater  circumferential  spread 
of  the  lines  of  force  of  bipolar  fields. 


§16]    FUNDAMENTAL  CALCULATIONS  FOR   WINDING.         51 

16.  Specific  Armature  Induction. 

Knowing  the  values  of  the  induction  per  unit  length  of 
active  armature  wire  under  unit  conditions,  a  general  ex- 
pression can  now  easily  be  derived  for  the  "specific  armature 
induction"  at  any  given  conductor  speed  and  field  density. 
The  induction  per  unit  length  of  active  conductor,  in  any 
armature,  is 

/==  4-  x  vc  x  oe",     (24:) 

n'p 

where  e'    —  specific  induction  of  active  armature  conductor, 

in  volts  per  foot; 

e  =  unit  armature  induction  per  pair  of  armature  cir- 
cuits, in  volts  per  foot,  from  Table  IV. ; 
#'p  =  number  of  bifurcations  of  current  in  armature,  or 
number  of  pairs  of  parallel  armature  circuits; 
«'p  has  the  following  values,  to  be  multiplied 
by  the  number  of  independent  windings  in  case 
of  multiplex  grouping  (§  44): 

#'p  —  i  for  bipolar  dynamos  and  for  multipolar  ma- 
chines having  ordinary  series  grouping, 
#'p  =  ;zp  for  multipolar  dynamos  with  parallel  group- 
ing, np  being  the  number  of  pairs  of  mag- 
net poles, 

n'p  =    — -  for  multipolar  dynamo  with  series-parallel 
3   grouping,  ns  being  the  number  of  arma- 
ture circuits  connected  in  series  in  each 
of  the  2n'p  parallel  circuits; 
vc    =  conductor-velocity,  or  cutting  speed,  in  feet  per 

second,  from  Table  V. ; 

3C"  =  field  density,  in  lines  of  force  per  square  inch, 
from  Table  VI. 

In  order  to  obtain  the  specific  armature  induction  in  the 
metric  system,  e  is  to  be  replaced  by  the  corresponding  value 
of  <?!,  Table  IV. ;  the  conductor  velocity  is  to  be  expressed  in 
metres  per  second,  Table  V.,  and  the  field  density,  OC,  in  lines 
per  square  centimetre,  from  Table  VII. ;  then  (24)  gives 
the  specific  armature  induction  in  volts  per  metre  of  active 
conductor. 


DYNAMO-ELECTRIC  MACHINES. 


[§17 


17.  Conductor-Telocity. 

Since  it  is  cheapest  to  increase  the  E.  M.  F.  of  a  dynamo 
by  raising  its  speed,  it  will  be  best  economy  to  run  a  dynamo 
at  as  high  a  conductor  velocity  as  practically  possible.  The 
cutting  speed  of  an  armature  is  limited  mechanically  as  well  as 
electrically;  friction  in  the  bearings,  strain  in  the  revolving 
parts  due  to  centrifugal  force,  and  heating  of  the  armature, 
caused  by  hysteresis  and  eddy  currents  in  the  iron,  play  an 
important  part  in  determining  the  proper  conductor  velocity. 
Furthermore,  if  the  number  of  revolutions  of  the  armature  is 
fixed,  either  by  its  mechanical  limit  or  by  the  speed  of  the 
engine  in  case  of  a  steam  dynamo,  or  otherwise,  then  the 
above  mechanical  and  electrical  limitations  alone  are  not  suffi- 
cient for  choosing  the  cutting  speed,  for,  too  high  a  velocity, 
for  instance,  permissible  from  all  other  considerations,  would 
excessively  increase  the  diameter  of  the  armature,  and  con- 
sequently would  bring  the  size  of  the  whole  machine  entirely 
out  of  proportion  to  its  output. 

TABLE  V. — MEAN  CONDUCTOR  VELOCITIES. 


CONDUCTOR  VELOCITY,  IN  FEET 

CONDUCTOR  VELOCITY,  IN  METRES 

PER  SECOND. 

PER  SECOND. 

CAPACITY 

IN 

BELT  -DRIVEN  DYNAMOS. 

BELT-DRIVEN  DYNAMOS. 

Direct- 

Direct- 

KILOWATTS. 

Driven 

Driven 

Drum 

Ring 

Dynamo. 

Drum 

Ring 

Dynamo. 

Armature. 

Armature. 

Armature. 

Armature. 

.1 

25 

50 

7.5 

15 

.25 

30 

55 

9 

16.5 

.5 

32 

60 

10 

18 

1 

35 

65 

11 

19.5 

2.5 

40 

70 

25 

12 

21 

'7.5 

5 

45 

75 

26 

13.5 

22.5 

8 

10 

50 

80 

28 

15 

24 

8.5 

25 

50 

80 

30 

15 

25 

9 

50 

50 

85 

32 

15 

25.5 

10 

100 

50 

85 

35 

15 

26 

11 

200 

50 

88 

40 

15 

26.5 

12 

300 

50 

90 

42 

15 

27 

12.5 

400 

92 

44 

27.5 

13 

600 

95 

45 

28 

13.5 

800 

95 

45 

28.5 

13.5 

1,000 

95 

45 

29 

13.5 

1,500 

100 

45 

30 

13.5 

2,000 

100 

45 

30 

13.5 

§18]     FUNDAMENTAL  CALCULATIONS  FOR   WINDING.        53 

In  modern  high-speed  (belt-driven)  dynamos  the  value  of  vc, 
for  drum  armatures,  varies  from  25  to  50  feet  per  second,  and 
for  ring  armatures,  which  offer  a  better  ventilation  and  are 
much  lighter  than  drum  armatures  of  the  same  diameter, 
ranges  between  50  and  100  feet  per  second.  In  low-speed" 
(direct-driven)  machines,  velocities  from  25  to  50  feet  per 
second  are  employed. 

In  Table  V.  (see  opposite  page)  average  values  of  VQ  for  vari- 
ous classes  and  sizes  of  dynamos  are  compiled. 

18.  Field  Density. 

The  specific  strength  of  the  magnetic  field  has  to  be  chosen 
according  to  the  size  of  the  machine,  the  number  of  poles,  the 
form  of  the  armature,  and  to  the  material  of  the  polepieces. 
In  general,  the  higher  a  density  of  the  magnetic  lines  per  unit 
of  field  area  is  taken,  the  larger  the  output  of  the  dynamo 
and  the  greater  the  number  of  poles,  in  multipolar  machines 
higher  values  of  3C  being  admitted  than  in  bipolar  ones.  In 
dynamos  with  smooth-core  armatures  the  field  densities  are 
taken  greater  than  in  those  with  toothed-armature  bodies,  for 
the  reason  that  in  the  latter  a  portion  of  the  lines  enters  the 
teeth  and  passes  from  tooth  to  tooth  without  cutting  the  con- 
ductors, and  that  in  such  armatures  it  therefore  takes  more 
lines  per  square  inch  of  pole  area  to  produce  the  same  field 
density  (per  square  inch  of  area  occupied  by  armature  con- 
ductors) than  for  smooth  cores;  consequently,  smaller  field 
densities  must  be  employed  with  toothed  armatures  in  order 
to  prevent  over-saturation  of  the  polepieces,  and,  eventually, 
of  the  frame.  This  leakage  through  the  armature  teeth  takes 
place  in  the  higher  a  degree  the  greater  the  width  of  the 
teeth  compared  to  that  of  the  slots,  and  therefore  still  smaller- 
field  densities  are  to  be  chosen  in  case  of  armature  cores  with 
tangentially  projecting  teeth,  and  of  those  with  closed  slots. 
Finally,  in  machine  having  wrought  iron  or  steel  polepieces, 
the  densities  can  be  taken  about  fifty  per  cent,  higher  than 
those  with  cast  iron  pole  shoes. 

The  suitable  values  of  3C"  for  all  these  various  cases  are 
tabulated  in  Table  VI.,  which  gives  the  average  densities  in 
lines  of  force  per  square  inch,  while  Table  VII.  contains  the 
corresponding  values  of  3C  in  lines  per  square  centimetre. 


54 


D  YNA  MO -EL  E  C  TRIG  MA  CHINES. 


[§18 


For  low-potential  and  for  high-amperage  machines  (electro- 
plating dynamos,  battery  motors,  large  incadescent  generators, 
etc.),  about  two-thirds  of  the  densities  given  in  Tables  VI. 
and  VII.  are  to  be  taken: 

TABLE  VI. — PRACTICAL  FIELD  DENSITIES,  IN  ENGLISH  MEASURE. 


Field  Densities,  in  Lines  of  Force  per  square  Inch 


Bipolar  Dynamos 


PolrpiecM  PoUpiMM  PokpheM 


Toothed  Armature  Core 


Straight  1 


Projecting  Teeth 


Cut       IWr'tlroD 


Multipolar  Dynamc 


CM        WVl  Iron 
lro»         orSU.1 


Pol.piwt,  PoU|>iecM  PoIepi.cM  Pol.pl.cn 


Toothed  Armature  Core 


Cut        Wr't  Irou 
Iron          or  Steel 


.1 

.2E 
.5 

1 

2.5 
5 

7.5 
10 


100 
800 

aoo 

500 
1000 
8000 


10000 

12000 


14000 


15000 


30000 


15000 
16000 
17000  25000 
26000 
19000 


20000 
22000 
04000 
27000 
80000 


80000 


86000 


45000 


8000 
10000 
12000 
13000 
14000 
15000 
16000 
17000 
18000 
20000 
22000 
24000 
27000 


12000 
15000 
18000 
19000 


27000 
30000 


40000 


10000 


12000 
13000 
14000 


18000 


12000 
14000 
15000 
16000 
18000 


22000 


14000 


18000 
19000 
20000 
21000 


24000 
26000 
28000 
30000 
32000 
35000 
38000 
41000 
45000 


20000 
24000 
27000 


30000 


35000 


41000 
44000 
47000 


56000 


12000 
14000 
16000 
17000 
18000 
19000 
20000 
21000 
22000 
23000 
25000 
27000 
29000 
31000 
33000 
35000 


18000 
21000 
24000 


30000 


35000 


40000 
42000 
44000 
46000 
48000 
50000- 


10000 
11000 
12000 
13000 
14000 
15000 
16000 
17000 
18000 
19000 


24000 


15000 
16000 
18000 
20000 
21000 
23000 
24000 


28000 


.1 

.25 
.5 
1 

2.5 
5 

7.5 
10 


100 
200 


1000 
2000 


TABLE  VII. — PRACTICAL  FIKLD  DENSITIES,  IN  METRIC  MEASURE. 


Field  Densities,  in  Lines  of  Force  per  sqmvre  Centimetre  . 


Bipolar-Dynamos 


Toothed  Armature  Core 


BtnJght  Teeth         Projecting  Teeth 


as 


PoUpltcM  PobpUcM 


Multipolar  Dy 


Smooth 

Armature 

Core 


Toothed  Armature  Core 


EC 


3 

.2! 

.6 
1 

2.5 
5 

7.5 
10 
25 
50 
100 
900 
300 
500 
1000 
8000 


1550 
1850 
2150 


2500 


3100 
8400 
8700 


4700 


2300 
2800 
8100 


4000 


4700 
5100 

6600 


7000 


1250 
1550 
1850 
2000 
2150 


8100 
8400 
8700 


1850 


8100 
3400 
3700 


4700 
5100 
5600 


1400 
1550 
1700 
1850 
2000 
2150 


2800 
8100 


2150 
2300 


2500 


3100 


3700 


4700 


2150 
2500 


3100 
3250 
3400 
8700 
4000 
4350 
4700 
5000 
5400 
5900 
6400 
7000 


3100 
3700 
4200 
4350 
4500 
4700 
5000 
5400 
5900 
6400 
6800 
7300 
7750 
8200 
8700 


1850 
2150 
2500 
2650 


3100 


4200 
4500 
4800 
5100 
5400 


3700 
8850 
4000 
4350 
4700 
5000 
5400 


6500 
6800 
7200 
7500 
7800 


1700 
1850 


2150 
2300 
2500 


3100 
8400 
8700 


2500 
2800 
8100 


3500 
3700 


4000 


4700 
5000 


.1 

,26 
.5 
*1 

2.5 

5 

7.5 
10 


100 


500 
1000 
2000 


§19]     FUNDAMENTAL  CALCULATIONS  FOR   WINDING.        55 

19,  Length  of  Armature  Conductor. 

By  means  of  the  specific  armature  induction  obtained  from 
formula  (24),  the  total  length  of  active  wire  to  be  wound  upon 
the  pole-facing  surface  of  any  armature  can  be  readily  deter- 
mined. If  E'  denotes  the  total  E.  M.  F.  generated  in  an 
armature,  and  Za  the  total  length  of  active  wire  wound  on  it, 
then  E1  divided  by  Za  will  give  the  specific  armature  induction, 
e'.  The  length  of  active  conductor  for  any  armature  can 
therefore  be  obtained  from  the  formula 


in  which  Za  =  total  length  of  active  conductor  (on  whole  cir- 
cumference opposite  polepieces),  in  feet,  or 
in  metres; 

E!  =  total  E.  M.  F.  to  be  generated  in  armature, 
i.  <?.,  volt  output  plus  additional  volts  to  be 
allowed  for  internal  resistances  (see  Table 
VIII.);  and 

e'  =  specific  induction  of  active  armature  wire,  cal- 
culated by  formula  (24),  in  volts  per  foot,  or 
in  volts  per  metre,  respectively. 

Introducing  the  value  of  e'  from  (24)  into  (25),  the  formula 
for  the  length  of  active  armature  conductor  becomes: 


N/    *7t      *s/    TT1  ^  ^^       ^    ^^ 

f         y^v      ^c      ^N     '-TV' 

^P 

The  length  Zais  obtained  in  feet,  if  e  is  given  in  volts  per  foot, 
vc  in  feet  per  second,  and  3C"  in  lines  per  square  inch;  and  is 
obtained  in  metres,  if  e  is  replaced  by  el  in  volt  per  metre, 
7>c  expressed  in  metres  per  second,  and  if  oc"  is  replaced  by  5C 
in  lines  per  square  centimetre. 

To  find  the  total  electromotive  force,  E',  to  be  generated 
by  the  armature,  increase  the  electromotive  force  E  wanted 
in  the  external  circuit,  by  the  percentages  given  in  Table  VIII. 
The  figures  in  the  second  column  of  this  table  refer  to  shunt- 
wound  dynamos,  and,  therefore,  take  into  account  the  arma- 
ture resistance  only.  The  percentages  in  the  third  and  fourth 


DYNAMO-ELECTRIC  MACHINES. 


[§20 


columns  are  to  be  used  for  series-  and  for  compound-wound 
dynamos  respectively,  and,  consequently,  include  allowances 
for  armature  resistance  as  well  as  for  series  field  resistance: 

TABLE  VIII. — E.  M.  F.  ALLOWED  FOR  INTERNAL  RESISTANCES. 


ADDITIONAL  E.  M.  F.  IN  PER  CENT.  OF  OUTPUT  E.  M.  F. 

CAPACITY 

IN  KILOWATTS. 

Shunt  Dynamos. 

Series  Dynamos. 

Compound 
Dynamos. 

Up  to            .5 

20  %  to  12  % 

40  %  to  25  % 

30  %  to  20  % 

1 

12 

10 

25 

20 

20 

15 

2.5 

10 

8 

20 

16 

15 

12 

*.-  ' 

5 

8 

7 

16 

14 

12 

10 

10 

7 

6 

14 

12 

10 

8 

25 

6 

5 

12 

10 

8 

7 

50 

5 

4 

10 

8 

7 

6 

100 

4 

3i 

8 

6 

6 

5 

200 

3| 

3 

6 

5 

5 

4 

500 

3 

2i 

5 

4 

4 

3 

1,000 

3i 

2 

4 

3 

3 

2i 

2,000 

2 

H 

3 

8* 

2* 

2 

20.  Size  of  Armature  Conductor. 

The  sectional  area  of  the  armature  conductor  is  determined 
by  the  strength  of  the  current  it  has  to  carry.  For  general 
work  the  current  densities  usually  taken  vary  between  400  and 
800  circular  mils  (.25  to  .5  square  millimetre)  per  ampere;  in 
special  cases,  however,  a  conductor  area  may  be  provided  at 
the  rate  of  as  low  as  200  to  400  circular  mils  (.125  to  .5  square 
millimetre)  per  ampere,  or  as  high  as  800  to  1,200  circular  mils 
(•5  to  .75  square  millimetre)  per  ampere.  The  low  rate  refers 
to  machines  which  only  are  to  run  for  a  short  while  at  the  time, 
as,  for  instance,  motors  to  drive  special  machinery  (private 
elevators,  pumps,  sewing  machines,  dental  drills,  etc.),  while 
the  high  rate  is  to  be  employed  for  dynamos  which  have  a 
fifteen  or  twenty  hours'  daily  duty,  as  is  the  case  for  central- 
station,  power-house,  and  marine  generators,  etc. 

Taking  600  circular  mils  per  ampere  as  the  average  current 
density  (=  475  square  mils,  or  .000475  square  inch  per  ampere, 
or  about  2,100  amperes  per  square  inch),  the  sectional  area  of 
the  armature  conductor,  in  circular  mils,  is  to  be 


§20]     FUNDAMENTAL  CALCULATIONS  FOR   WINDING.        57 

......  (37) 


where  #a2  =  sectional  area  of  armature  conductor,  in  circular 

mils; 

6&  =  diameter  of  armature  wire,  in  mils; 
/'  =  total  current  generated  in  armature,  in  amperes; 

and 
«'p  =  number  of  pairs  of  parallel  armature  circuits. 

In  the  metric  system,  taking  .4  square  millimetre  per  am- 
pere (=  2.$  amperes  per  square  millimetre)  as  the  average 
current  density  in  the  armature  conductor,  the  sectional  area 
of  the  inductor,  in  square  millimetres,  is  obtained  : 


from  which,  in  case  of  a  circular  conductor,  the  diameter  can 
be  derived  : 


The  size  of  conductor  may  be  taken  from  the  wire  gauge 
tables  by  selecting  a  wire,  the  sectional  area  of  one  or  more 
of  which  makes  up,  as  nearly  as  possible,  the  cross-section 
obtained  by  formula  (27). 

The  total  armature  current,  /',  in  shunt  and  compound 
dynamos  is  the  sum  of  the  current  output,  /,  and  the  exciting 
current  of  the  shunt  circuit.  The  latter  quantity,  however, 
generally  is  very  small  compared  with  the  former,  and  in  all 
practical  cases,  consequently,  it  will  be  sufficient  to  use  the 
given  /  instead  of  the  unknown  /'  for  the  calculation  of  the 
conductor  area.  A  supplementary  allowance  may,  then,  be 
made  by  correspondingly  rounding  off  the  figures  obtained 
by  (27),  or  by  selecting  the  wires  of  such  a  gauge  that  the 
actual  conductor  area  is  somewhat  in  excess  of  the  calculated 
amount. 


CHAPTER   IV. 

DIMENSIONS    OF    ARMATURE    CORE. 

21.  Diameter  of  Armature  Core. 

If  the  speed  of  the  dynamo  is  given,  the  proper  conductor 
velocity  taken  from  Table  V.  will  at  once  determine  the 
diameter  of  the  armature.  Let  JV  denote  this  known  speed, 
in  revolutions  per  minute,  and  d'&  the  mean  diameter  of  the 


Fig-  45' — Principal  Dimensions  of  Armature. 

armature  winding,  in   inches,  then  the  cutting  speed,  in  feet 
per  second,  is 

d\  X  n  .  .  N 


12 


from  which  follows: 


(30) 


In  the  metric  system  the  mean  diameter  of  the  armature 
winding,  in  centimetres,  is  given  by 

100  X  60        v0  vf 

d\  =  ~  ~-  -  X  ^  =  1,900  X  ^,       . .   .(31) 

in  which  vc  is  to  be  expressed  in  metres  per  second. 

58 


§21] 


DIMENSIONS  OF  ARMATURE   CORE. 


59 


From  this  mean  winding  diameter,  </'a,  then,  the  diameter 
of  the  armature  core,  d&,  Fig.  45,  is  found  by  making  allow- 
ance for  the  height  of  the  armature  winding.  For  small 
armatures — under  two  feet  in  diameter — the  coefficients  given 
in  the  following  Table  IX.  may  be  used  for  this  purpose;  for 
larger  ones  it  is  sufficient  to  simply  round  off  the  result  of 
formula  (30),  or  (31),  respectively,  to  the  next  lower  round 
figure: 


TABLE  IX. — RATIO  BETWEEN  CORE  DIAMETER  AND  MEAN  WINDING 
DIAMETER  FOR  SMALL  ARMATURES. 


SIZE  OF  ARMATURE  . 

RATIO  *• 
da, 

English  Measure. 

Metric  Measure. 

Drum  Armatures. 

Ring  Armatures. 

Up  to    2  ins.  dia. 

Up  to    5  cm.  dia. 

.88 

_ 

4 

10 

.92 

.95 

8 

20 

.94 

.97 

12 

30 

.95 

.975 

16 

40 

.96 

.98 

20 

50 

.965 

.9825 

24 

60 

.97 

.985 

For  dynamos  with  internal  poles,  the  reciprocals  of  these 
coefficients  are  to  be  taken,  or  the  result  is  to  be  rounded  off 
to  the  next  higher  round  figure,  respectively;  and  the  dimen- 
sion thus  obtained  is  the  internal  diameter  of  the  armature 
core.  In  the  case  of  machines  with  internal  as  well  as  external 
poles,  the  mean  winding  diameter,  d'&,  is  identical  with  the 
mean  diameter  of  the  armature  body. 

If  the  speed  of  the  dynamo  is  not  prescribed  by  the  condi- 
tions for  its  service,  the  following  Tables  X.,  XL,  and  XII. 
will  be  found  useful.  Table  X.  gives  practical  data  for  speeds, 
conductor  velocities,  and  corresponding  diameters  of  drum 
armatures.  Table  XI.  contains  similar  information  relating 
to  high-speed  ring  armatures,  and  in  Table  XII.  data  for  the 
speeds  of  low-speed  ring  armatures  are  compiled  and  the  cor- 
responding armature  diameters  computed: 


60  DYNAMO-ELECTRIC  MACHINES.  [§21 

TABLE  X. — SPEEDS  AND  DIAMETERS  OP  DRUM  ARMATURES. 


ENGLISH  MEASURE. 

METRIC  MEASURE. 

CAPACITY 

SPEED, 

IN 

IN 

KILOWATTS. 

REVOLUTIONS 

PBR 

MINUTE. 

w 

Conductor 
Velocity, 
in  ft.  per  sec. 

Vc 

Armature 
Diameter, 
in  inches. 
da, 

Conductor 
Velocity, 
in  m.  per  sec. 

Vc 

Armature 
Diameter, 
in  cm. 
da 

.1 

3,000 

25 

11 

8 

4.5 

.25 

2,700 

30 

2 

9 

5.5 

.5 

2,400 

32 

^ 

10 

7 

\ 

2,200 

34 

3 

11 

8.5 

2 

2,000 

36 

a 

12 

10 

3 

1,900 

40 

4i 

13 

12 

5 

1,800 

45 

5: 

14 

14 

10 

1,700 

50 

6 

15 

16 

15 

1,600 

50 

6f 

15 

17 

20 

1,500 

50 

3 

15 

18 

25 

1,350 

50 

s| 

15 

20 

30 

1,200 

50 

9 

15 

23 

50 

1,050 

50 

101 

15 

2ii 

75 

900 

50 

121 

15 

30 

100 

750 

50 

15 

15 

37 

150 

600 

50 

18i 

15 

46.5 

200 

500 

50 

22^ 

15 

56 

3UO 

400 

50 

28 

15 

70 

TABLE  XI. — SPEEDS  AND  DIAMETERS  OF  HIGH-SPEED  RING 
ARMATURES. 


ENGLISH  MEASURE. 

METRIC  MEASURE. 

CAPACITY 

SPEED, 

IN 

IN 

REVOLUTIONS 

PER 

Conductor 

Armature 

Conductor 

Arm-tture 

KILOWATTS. 

MINUTE. 

^V 

Velocity, 
in  ft.  per  sec. 

Diameter, 
in  inches. 

Velocity, 
in  m.  per  sec. 

Diameter, 
in  cm. 

Vc 

da 

Vc 

da 

.1 

2,600 

50 

4 

15 

10 

.25 

2,400 

55 

5 

17 

12.5 

.5 

2,200 

60 

6 

18.5 

15 

1 

2,000 

65 

7 

20 

18 

2.5 

1,700 

70 

9 

21.5 

23 

5 

1,500 

75 

11 

23 

28 

10 

1,250 

80 

14 

24 

35 

25 

1,000 

80 

18 

25 

46 

50 

800 

85 

24 

26 

60 

100 

600 

85 

32 

26 

80 

200 

500 

88 

40 

27 

100 

300 

450 

90 

46 

28 

115 

400 

•  400 

92 

52 

28 

130 

600 

350 

95 

62 

28 

150 

800 

300 

95 

72 

29 

180 

1,000 

250 

95 

87 

30 

225 

1,500 

225 

100 

102 

30 

250 

2,000 

200 

100 

115 

32 

300 

§22] 


DIMENSIONS   OF  ARMATURE   CORE. 


61 


TABLE  XII.— SPEEDS  AND  DIAMETERS  OF  LOW-SPEED  RING 
ARMATURES. 


ENGLISH  MEASURE. 

METRIC  MEASURE. 

n 

SPEED, 

O  AP  AC  IT  Y 

IN 

IN 

REVOLUTIONS 

Conductor 

Armature 

Conductor 

Armature 

KILOWATTS. 

MINUTE. 

^Y 

Velocity, 
in  ft.  per  sec. 

Diameter, 
in  inches. 

Velocity, 
in  m.  per  sec. 

Diameter, 
in  cm. 

2.5 

400 

25 

14 

7.5 

35 

5 

350 

26 

17 

8 

42 

10 

300 

28 

21 

8.5 

53 

25 

250 

30 

27 

9 

70 

50 

200 

32 

36 

9.5 

90 

100 

175 

35 

46 

11 

115 

200 

150 

40 

60 

12 

150 

300 

125 

42 

78 

13.25 

200 

400 

100 

44 

100 

13.25 

250 

600 

90 

45 

115 

13.75 

290 

800 

80 

45 

129 

13.75 

325 

1,000 

75 

45 

138 

13.75 

350 

1,500 

70 

45 

148 

13.75 

375 

2,000 

65 

45 

158 

13.75 

400 

22.  Dimensioning  of  Toothed    and  Perforated  Arma- 
tures. 

Armatures  with  toothed  and  with  perforated-core  discs, 
which  have  been  much  used  in  recent  years,  offer  the  following 
advantages  over  smooth  armatures:  (i)  Excellent  means  for 
driving  the  conductors;  (2)  mechanical  protection  of  the 
winding,  especially  in  cores  with  tangentially  projecting 
teeth,  and  in  perforated  bodies;  (3)  lessening  of  the  resistance 
of  the  magnetic  circuit,  and,  therefore,  saving  in  exciting 
power;  (4)  prevention  of  eddy  currents  in  the  conductors; 
(5)  lessening  of  the  difference  between  the  amounts  of  field- 
distortion  at  open  circuit  and  at  maximum  output,  and  there- 
fore possibility  of  sparkless  commutation  for  varying  load 
without  shifting  brushes;  and  (6)  taking  up  of  the  magnetic 
drag  by  the  core  instead  of  by  the  conductors.  Their  dis- 
advantages wct\  (i)  Increased  cost  of  manufacture;  (2)  neces- 
sity for  special  devices  to  insulate  the  winding  from  the  core; 

(3)  eddy  currents    set   up   by  the  teeth  in   the   polar   faces; 

(4)  additional   heat    generated    in    the   iron    projections    by 


62  DYNAMO-ELECTRIC  MACHINES.  [§22 

hysteresis;  (5)  increase  of  self-induction  in  short-circuited 
armature  coils  due  to  imbedding  them  in  iron,  especially  in 
high  amperage  machines;  (6)  increased  length  of  the  gap- 
space  and  consequent  greater  expenditure  in  exciting  power 
when  saturation  of  the  teeth  takes  place;  and  (7)  leakage  of 
lines  of  force  through  the  armature  core,  exterior  to  the 
winding,  particularly  in  case  of  projecting  teeth  and  of  per- 
forated cores. 

Comparing  these  advantages  and  disadvantages  with  each 
other  we  find  that  the  conditions  that  have  to  be  fulfilled  in 
order  to  bring  to  prominence  certain  advantages  will  also 
favor  the  conspicuousness  of  certain  of  the  disadvantages, 
and  moreover  we  see  that  what  is  an  advantage  in  one  case 
may  be  a  decided  disadvantage  in  another.  All  considered, 
therefore,  there  are  no  such  striking  advantages  in  either  the 
toothed  or  the  smooth  core  as  to  make  any  one  of  them 
superior  in  all  cases  over  the  other,  and  a  general  decision 
whether  a  toothed  or  a  smooth-core  armature  is  preferable, 
cannot  be  arrived  at.  As  a  matter  of  fact,  in  practice  it 
chiefly  depends  upon  the  purpose  of  the  machine  to  be 
designed  whether  a  smooth  or  a  toothed  core  is  preferably 
used  in  its  armature.  In  machines  with  toothed  and  with 
perforated  armatures  an  increase  of  the  load  has  the  effect  of 
increasing  the  saturation  of  the  iron  projections  and  therewith 
the  reluctance  of  the  air  gap;  the  counter-magnetomotive 
force  of  the  armature,  which  also  increases  with  the  load,  has 
therefore  to  overcome  a  greater  reluctance  as  it  increases 
itself,  in  consequence  of  which  the  demagnetizing  effect  of 
the  armature  is  kept  very  nearly  constant  at  all  loads.  Hence 
the  distribution  of  the  field  in  the  gap  remains  nearly  the  same 
and  the  angle  inclosed  between  the  planes  of  commutation  at 
no  load  and  at  maximum  output  is  reduced  to  a  minimum. 
For  cases  where  sparkless  commutation  is  required  without 
shifting  the  brushes  for  varying  loads,  as  for  instance  in  rail- 
way generators,  in  which  due  to  the  continual  and  sudden 
fluctuations  of  the  load  a  shifting  of  the  brushes  is  impractica- 
ble, the  employment  of  toothed  armatures  is  preferable,  for 
the  attainment  of  the  desired  end  in  this  case  outweighs  all 
their  disadvantages.  On  the  other  hand,  the  self-induction  in 
smooth-core  armatures,  owing  to  the  absence  of  iron  between 


§  22]  DIMENSIONS  OF  ARM  A  TURE    CORE.  63 

the  conductors,  is  much  less,  and  consequently  they  are  chosen 
in  cases  of  machines  in  which  large  currents  are  commutated 
at  low  voltages,  such  as  in  central  station  lighting  generators 
and  in  electro-metallurgical  machines.  In  the  latter  case  the 
disadvantage  of  increased  self-induction  in  the  toothed  arma- 
ture is  the  main  consideration  and  drives  it  out  of  competi- 
tion with  the  smooth  armature,  in  spite  of  all  advantages  which 
it  may  have  otherwise.  Again,  in  the  case  of  motors,  where 
a  large  torque  is  the  desideratum,  especially  in  low-speed 
motors,  such  as  single  reduction  and  gearless  railway  motors, 
the  toothed  armature  answers  best,  as  in  this  instance  its 
advantage  of  increased  drag  upon  the  teeth  is  considered  the 
prominent  one.  Toothed  armatures  must  further  be  em- 
ployed if,  in  a  series  motor,  a  constant  speed  under  all  loads 
is  to  be  attained,  for  at  light  loads  the  teeth,  being  worked 
at  a  low  point  of  magnetization,  offer  but  little  reluctance  to 
the  flux  through  the  armature,  while  at  heavy  loads  the  teeth 
become  saturated  and  considerably  increase  the  reluctance  of 
the  magnetic  circuit,  thereby  preventing  the  induction  from 
increasing  with  increased  field  excitation,  the  result  being 
a  motor  that  comes  much  nearer  being  self-regulating  than 
one  with  a  smooth-core  armature. 

In  order  to  more  definitely  determine  the  mechanical  advan- 
tage of  the  iron  projections,  W.  B.  Sayers l  compared  the 
pull  on  the  conductors  in  toothed  and  smooth-core  armatures. 
He  found  that  in  toothed  armatures  the  driving  force  is  borne 
directly  by  the  iron  instead  of  by  the  conductors  as  in  case 
of  smooth-core  machines.  Taking  the  case  of  an  armature  in 
which  the  thickness  of  the  tooth  is  equal  to  the  width  of  the 
slot,  he  shows  that,  when  the  density  in  the  teeth  is  100,000 
lines  per  square  inch  (=  15,500  lines  per  square  centimetre), 
that  in  the  slots  is  about  300  lines  per  square  inch  (=  47  per 
square  centimetre),  while  in  a  smooth-core  armature  the  field 
density  would  be  about  50,000  per  square  inch  (=  7,750  per 
square  centimetre),  from  which  follows  that  the  force  acting 
upon  the  conductors  is  about  167  times  greater  in  the  latter  case 
than  in  the  former.  In  another  example  he  takes  a  higher  mag- 
netic density  and  finds  that  the  pull  in  case  of  the  toothed  arma- 


1  London  Electrician,  April    19,  1895;   Electrical  World,   vol.  xxv.  p.   562 
(May  n,  1895). 


64 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§22 


ture  is  only  16  times  as  great  as  in  a  corresponding  smooth 
armature.  If  the  density  is  so  high  that  the  teeth  become  satu- 
rated, the  field  density  in  the  slots  will  approach  that  in  the 
gap  of  an  equally  sized  smooth  armature,  and  the  forces  will 
be  about  equal  in  both  cases.1 

When  a  toothed  or  perforated  armature  is  placed  in  a  mag- 
netic field,  the  lines  of  force  concentrate  toward  the  teeth  in 
form  of  bunches,  Fig.  46,  and  thereby  destroy  the  uniformity 


Fig.  46. — Distribution  of  Magnetic  Fig.  47. — Distribution  of  Magnetic 
Lines  around  Toothed  Armature  Lines  around  Toothed  Armature 
at  Rest.  in  Motion. 

of  the  field.  If  the  armature  is  now  revolved  these  bunches 
are  taken  along  by  the  teeth  until  a  position,  Fig.  47,  is 
reached  in  which  the  lines  have  been  distorted  to  such  a 
degree  that  the  reluctance  of  their  path  has  reached  the 
maximum  value  the  magnetomotive  force  of  the  field  is  able 
to  overcome.  At  this  moment  each  bunch  of  lines  will  com- 
mence to  change  over  to  the  next  following  tooth  of  the  arma- 
ture, and  thus  every  line  of  each  bunch  will  in  succession 
cross  the  slot  immediately  behind  the  tooth  through  which  it 
had  passed  previously.  In  this  manner  every  line  of  force 
passing  through  the  armature  core  cuts  all  the  inductors  on 
the  armature  during  each  revolution.  By  the  action  of  chang- 
ing over  from  one  tooth  to  the  next,  an  oscillation  or  quiver- 
ing of  the  magnetic  lines  is  caused,  which  tends  to  set  up 
eddy  currents  in  the  teeth  and  in  the  polar  faces.  In  order  to 
obviate  excessive  heating  from  this  cause  it  is  necessary  that 


1  See  also  "  On  the  Seat  of  the  Electrodynamic  Force  in  Ironclad  Arma- 
tures," by  E.  J.  Houston  and  A.  E.  Kennelly,  Electrical  World,  vol.  xxviii. 
P-  3  (July  4,  1896).  Comment,  by  Townsend  Wolcott,  Electrical  World,  vol. 
xxviii.  p.  271  (September  5,  1896),  and  by  William  Baxter,  Jr.,  Electrical 
World,  vol.  xxviii.  p.  299  (September  12,  1896). 


§22] 


DIMENSIONS   OF  ARMATURE   CORE. 


the  teeth  must  be  made  numerous  and  narrow,  and  that  the 
length  of  the  air  gap  between  the  pole  face  and  the  top  of 
the  iron  projection  must  bear  a  definite  relation  to  the  width 
of  the  slot.  In  practice  it  has  been  found  that— according: 
to  the  field  density  employed — air  gaps  having  a  radial  length 
of  from  one-fourth  to  one-half  the  width  of  the  slot,  in  large 
and  medium  size  machines  respectively,  and  a  ratio  of  gap  to 
slot  up  to  i  in  very  narrow  slotted  small  armatures,  give  the 
best  results. 

a.    Toothed  Armatures. 

The  mean  winding  diameter,  d'&,  of  a  toothed  armature 
being  determined  by  means  of  formula  (30),  its  core  diameter  or 
diameter  at  bottom  of  slots,  dM  Fig.  48,  is  obtained  by  deduct- 


UMBER  OF  SLOTS 


Fig.  48. — Dimensions  of  Toothed  Core  Disc. 

ing  from  d 'a  the  height  of  the  winding  space,  or,  in  this  case, 
the  depth  of  the  slots,  hM  averages  for  which  are  given  in  the 
fourth  column  of  Table  XVIII.,  §  23.  The  outside  diam- 
eter of  the  armature,  d"w  over  the  teeth,  is  obtained  by  adding 
hM  from  Table  XVIII.  to  d'w  from  formula  (30). 

The  number  of  the  slots,  ri G,  since  practice  has  shown,  in  accord- 
ance with  the  theoretical  considerations,  that  better  results 
are  obtained  from  deep  and  narrow  slots  than  from  shallow 
and  wide  ones,  should  be  taken  as  large  as  possible,  from  the 
mechanical  and  economical  standpoint.  In  the  following 
Table  XIII.  good  practical  limits  of  the  number  of  slots  for 
armatures  of  different  diameters  are  given: 


66  DYNAMO-ELECTRIC  MACHINES.  [§22 

TABLE  XIII.— NUMBER  OF  SLOTS  IN  TOOTHED  ARMATURES. 


DIAMETER  OB 

ARMATURE. 

d' 

a 

NUMBER  OP  SLOTS. 
tt'c 

Inches. 

Centimetres. 

5 

12.5 

30  to  50 

10 

25 

40    70 

20 

50 

60   100 

30 

75 

100   150 

50 

125 

150   200 

100 

250 

200   300 

150 

375 

250   350 

200 

500 

300   400 

As  to  the  width  of  the  slots,  b&,  Fig.  49,  a.  number  of  conflict- 
ing conditions  governs  its  relation  to  that  of  the  teeth:  On 
account  of  the  tendency  of  the  teeth  to  create  eddy  currents 


Fig.  49> — Various  Types  of  Slots  for  Toothed  Armatures. 

in  the  pole  faces,  their  width  ought  to  be  small  compared  with 
that  of  the  slots,  or  shallow  slots  and  narrow  teeth  should  be 
used ;  in  order  to  reduce  the  hysteresis  loss  in  the  teeth  and 
the  heat  caused  by  the  same  to  a  minimum,  the  mass  of  the 
teeth  should  be  small  and  their  area  perpendicular  to  the  flow 
of  the  lines,  hence  their  width  should  be  large,  that  is,  on  this 
account  narrow  slots  and  wide  teeth  should  be  employed;  for 
the  sake  of  effectively  reducing  the  magnetic  reluctance  of  the 
circuit,  the  area  at  the  bottom  of  the  teeth  should  be  large, 
hence  the  slots  narrow  and  the  teeth  wide. 


§22]  DIMENSIONS   OF  ARMATURE   CORE.  67 

L.  Baumgardt1  proposes  to  calculate  the  hysteresis  heat  per 
unit  volume  of  the  teeth  for  a  variety  of  values  for  the  width 
of  the  slot,  also  to  find  that  width  of  slot  for  which  the  density 
in  the  teeth  for  given  armature-diameter,  number,  and  sec- 
tional area  of  slots  becomes  a  minimum,  and  to  compare  the 
values  so  found,  choosing  a  practical  width  that  is  not  too  far 
from  giving  minimum  hysteresis  heat  and  minimum  tooth 
density.  For  the  purpose  of  calculating  the  relative  values 
of  the  hysteresis  heat  for  a  given  width  of  the  slot  he  gives  a 
formula  which,  when  reduced  to  its  simplest  form,  becomes: 


Sa  X  (a^  X  A  —  Ss) 
the  symbol  A  standing  for  the  expression: 

7    It      _  ..f         .    x       £ 


(32) 


™a      7T~       f*  e   '>   wii 

2»'c  X  tan  — — 

^  c 

in  which  Y  =  hysteresis  heat  per  unit  volume  of  teeth  divided 
by  a  constant  that  depends  upon  the  machine 
under  consideration; 

d"&  =  external  diameter  of  armature  (in  millimetres) ; 
n'0  =  number  of  slots; 
bs  =  width  of  slots  (in  millimetres); 
Sa  —  sectional  area  of  slot  =  bs  X  h&  (in  millimetres). 
In  order  to  save  the  trouble  of  employing  this  rather  com- 
plicated formula-in  every  single  instance,  the  author  has  calcu- 
lated the  values  of  Ffor  £s  =  .75  to  25  mm.  (1/32  to  i  inch)  for 
a  variety  of  cases  ranging  from  d"^  =  100  mm.  (•=  4"),  n'c  = 
24,  SB=go  mm.2   (=   .14  square    inch)    to  d"&   =   5,000   mm. 
(  =197^*),  «'c  320,  Sa  =  2,500=  mm.2  (  =  3.875  square  inches), 
and    in  taking  the  minimum  value  of  Fin   each  armature  as 
unity,   has,  for  every  case,  plotted  a  curve  with  the  various 
widths  of  the  slot  as  abscissae  and  the  value  of 

F 


1  "  On  the  Dimensioning  of  Toothed  Armatures,"  by  Ludwig  Baumgardt, 
Elektrotechn.  Zeitschr.,  vol.  xiv.  p.  497  (September  I,  1893);  Electrical  World, 
vol.  xxii.  p.  234  (September  23,  1893). 


68 


D  YNA MO-ELECTRIC  MA  CHINES. 


[§22 


as  ordinates.  In  Fig.  50  these  curves  are  arranged  in  four 
groups  with  reference  to  the  size  of  the  armature,  only  the 
two  limiting  curves  of  each  group  being  drawn.  They  show 
that  the  specific  hysteresis  heat  at  first  diminishes  slightly  as 
the  width  of  the  slot  increases  and  arrives  at  a  minimum  point 


y^.Vn  %    3/i6    M          h  %  %        \ 

WIDTH   OF  SLOT 

Fig.  50. — Variation  of  Hysteresis  Heat  per  Unit  Volume  of  Teeth  with 
Increasing  Width  of  Slot,  for  different  Sizes  of  Toothed  Armatures. 

which  over  the  whole  range  lies  between  the  narrow  limits  of 
1/16  and  3/16  inch  (1.5  and  5  mm.)  width  of  slot,  after  which  it 
increases  very  rapidly  in  case  of  small  armatures,  and  more  or 
less  slowly  in  case  of  large  ones.  Since  a  slot  of  1/16  inch 
(1.5  mm.)  width  is  too  small  for  even  the  smallest  armature  and 
one  of  3/16  inch  (4.5  mm.)  is  too  small  for  anything  but  a  very 
small  machine,  it  follows  that  the  minimum  of  hysteresis  heat- 
ing cannot  be  reached  in  practice,  but  by  making  the  slots 
narrow  and  deep  the  hysteresis  effect  can  be  kept  within  prac- 


322] 


DIMENSIONS   OF  ARMATURE    CORE. 


69 


tical  limits.  The  width  of  the  slot  having  been  chosen,  the 
limits  of  the  specific  hysteresis  heat,  expressed  as  multiples  of 
the  minimum  value,  can  then  be  obtained  from  the  curves  in 
Fig.  50,  or  from  the  following  Table  XIV.,  which  has  been 
compiled  from  the  curves  given: 

TABLE  XIV. — SPECIFIC  HYSTERESIS  HEAT  IN  TOOTHED  ARMATURES, 
FOR  DIFFERENT  WIDTHS  OF  SLOTS. 


RELATIVE  SPECIFIC  HYSTERESIS  HEAT  IN  TEETH. 

WIDTH  OF  SLOT. 

4"  to  10" 

10°  to  40" 

40"  to  120" 

120"  to  200" 

(100  to  250 

(250  to  1,000 

(1,000  to  3,000 

(3,000  to  5,000 

mm.) 

mm.) 

mm.) 

mm.) 

Inch. 

Millimetres. 

Armature. 

Armature. 

Armature. 

Armature. 

A 

0.75 

H  to  3 

li  to  2i 

li  to  2i 

Iito2 

A 

1.5 

1     '  li 

li      2 

H       2 

li'     If 

i 

* 

l     '  li 

1       H 

1       H 

li'     H 

A 

4.5 

li  '  2 

1       H 

l       H 

1     '     li 

6 

li  '  3 

li      2 

H     if 

1     '     li 

-1 

9.25 

2i   '  10 

li      3i 

li     2* 

H'     H 

£ 

12.5 

4     '  20 

2i      6i 

If      3 

li'    2 

f 

16 

6     '  25 

3f      12 

2i      4 

If    2i 

f 

18.5 

4f      18 

2f      5 

li'    3 

1 

22 



6        22 

3f      7 

If    4 

i 

25 



5        12 

2    '    6 

According  to  this  table  the  specific  heat  due  to  hysteresis,  if, 
for  instance,  a  ^  inch  (18.5  mm.)  slot  is  used  in  a  100  inch 
(2,500  mm.)  armature,  is  from  2^  to  5  times  as  high  as  in  case 
of  a  y%  inch  (3  mm.)  slot  for  which,  in  that  group,  it  is  a  mini- 
mum. 

The  value  of  bm  for  which  the  magnetic  density  in  the  teeth 
becomes  a  minimum,  is  found  by  making  the  circumferential 
width  at  the  bottom  of  the  teeth, 


n 


=7t  ( 


=7t     d"    - 


-  n'c  X 


a  maximum;  and  the  value  of  bB  which  does  the  latter  is 


v  =  .  /?_»•  x  s\ 


(33) 


DYNAMO-ELECTRIC  MACHINES. 


[§22 


where  b\  =  width  of  slot  for  minimum  tooth  density,  in  inches 

or  in  centimetres; 
S"s  =  cross-section  of  slot,  in  square  inches,  or  in  square 

centimetres; 
n'c  =  number  of  slots. 

While  formula  (33)  in  connection  with  Table  XIV.  is  very 
useful  for  the  determination  of  the  best  width  of  the  slots  in 
case  their  cross-section  is  given,  ordinarily  the  problem  is  to 
be  attacked  by  first  selecting  the  number  of  teeth,  then  deter- 
mining the  width,  and  finally  the  depth  of  the  slot.  Consider- 
ing all  the  adverse  conditions,  the  author  has  found  it  a  good 
practical  rule  to  make  the  width  .of  the  slots 


*.= 


X  it 


2    X 


TABLE  XV.— DIMENSIONS  OP  TOOTHED  ARMATURES,  IN  ENGLISH 
MEASURE. 


DIAMETER 

DIMENSIONS  OP  SLOTS. 

NUMBER  OP 

CORE 

WIDTH  AT 

OP 

SLOTS. 

DIAMETER, 

BOTTOM  OF 

ARMATURE, 
IN  INCHES. 

Depth, 
in  inches. 

Width, 
in  inches. 

Ratio 
of  Depth  to 

»v= 

IN  INCHES. 

TOOTH, 
IN  INCHES. 

Width. 

to  a  «t 

t*a    *i       j^ 

d\ 

ft. 

ba 

268 

d\-2h& 

n'c 

5 

f 

j 

2.50 

30 

84 

.14 

6 

¥ 

2.59 

36 

4f 

.14 

8 

3 

2.66 

44 

H 

.18 

10 

7 

it 

2.95 

52 

.20 

12 

1 

A 

3.20 

60 

10 

.21 

15 

1 

§¥ 

3.43 

72 

12f 

.23 

18 

li 

11 

3.64 

80 

.26 

21 

1 

1 

3.66 

88 

m 

-.28 

25 

li 

¥ 

3.69 

98 

22 

.30 

30 

1 

3.71 

108 

27| 

.37 

40 

If 

15 

3.73 

136 

36^ 

.38 

50 

IT 

^ 

3.75 

160 

46-1 

.41 

60 

2 

17 

3.76 

180 

56 

.45 

70 

$1 

A 

3.78 

196 

65f 

.51 

80 

2J 

9 

3.79 

212 

75-|- 

.52 

90 

24 

4 

228 

85 

.55 

100 

2f 

it 

4 

232 

94^ 

.59 

125 

3 

i 

4 

264 

119 

.67 

150 

34 

7 

4 

272 

143 

.78 

200 

4 

1 

4 

320 

192 

.89 

§22] 


DIMENSIONS  OF  ARMATURE    CORE. 


that  is  to  say,  to  make  the  width  of  the  slots  equal  to  half 
their  pitch  on  the  outer  circumference,  for  the  special  case  of 
a  straight-tooth  core,  then  the  width  of  the  slots  is  equal  to 
the  top  width  of  the  teeth. 

The  proper  sectional  area  S\  of  the  slots  to  accommodate  a~ 
sufficient  amount  of  armature  winding  is  obtained  by  making 
the  depth  of  the  slot  from  2^  to  4  times  its  width,  according 
to  the  size  of  the  armature,  the  minimum  value  referring  to 
very  small  and  the  maximum  value  to  the  largest  machines. 

Applying  these  rules  to  armatures  of  various  sizes,  the  ac- 
companying Tables  XV.  (see  page  70)  and  XVI.  have  been 
calculated,  giving  the  dimensions  of  toothed  armatures,  the 
former  in  English  and  the  latter  in  metric  measure: 

TABLE  XVI. — DIMENSIONS  OF  TOOTHED  ARMATURES,  IN  METRIC 
MEASURE. 


I 

DIAMETER 

OF 

DIMENSIONS  OF  SLOTS. 

NUMBER  OP 
SLOTS. 

CORE 
DIAMETER, 

WIDTH  AT 
BOTTOM  op 

ARMATURE, 

Depth, 

Width, 

Ratio 

n'c   = 

IN  CM. 

TOOTH, 
IN  CM. 

IN  CM. 

in  cm. 

in  cm. 

of  Depth  to 
Width 

d!"a7r 

d&  = 

d&  TT 

d\ 

Aa 

*s 

7*a  :  l>* 

2&s 

d\  -  2h& 

n'c        ** 

10 

1.5 

.6 

2.50 

24 

7 

.32 

15 

1.75 

.65 

2.69 

36 

11.5 

.36 

20 

2 

.7 

2.86 

44 

16 

.44 

25 

2.25 

.75 

3.00 

52 

20.5 

.49 

30 

2.5 

.8 

3.13 

60 

25 

.51 

40 

3 

.9 

3.34 

70 

36 

.72 

50 

3.5 

1.0 

3.50 

78 

43 

.75 

60 

4 

1.1 

3.64 

86 

52 

.80 

75 

4.5 

1.2 

3.75 

98 

66 

.92 

100 

5 

1.3 

3.85 

120 

90 

1.06 

150 

5.5 

1.4 

3.95 

168 

139 

1.20 

200 

6 

1.5 

4.0 

210 

188 

1.32 

250 

7 

1.75 

4.0 

224 

236 

1.56 

300 

8 

2.0 

4.0 

236 

286 

1.81 

400 

9 

2.25 

4.0 

288 

382 

1.92 

500 

10 

2.5 

4.0 

320 

480 

2.21 

b.   Perforated  Armatures. 

The  same  considerations  that  prevailed  in  determining  the 
number  and  the  width  of  the  slots  in  toothed  armatures  are 
also  decisive  for  the  dimensioning  of  perforated  cores.  The 


DYNAMO-ELECTRIC  MACHINES. 


[§23 


number  of  perforations,  for  this  reason,  can  be  taken  in  the 
same  limits  as  the  number  of  slots  for  toothed  cores.  See 
Table  XIII. 

In  case  of  round  holes,  Fig.  51,  the  thickness  of  the  iron 
between  two  adjacent  perforations  should  be  taken  between 
0.4  and  0.75  times  the  diameter  of  the  hole. 

For  rectangular  holes,   Fig.    52,   the  thickness  of  the   iron 


0.56gT00.9&s 


Figs.  51  and  52. — Dimensions  of  Perforated-Core  Discs. 

between  them  is  to  be  taken  somewhat  greater  than  for  round 
holes,  namely,  from  0.5  to  0.9  times  the  width  of  the  channel. 
The  distance  of  the  holes  from  the  outer  periphery  is  to  be 
made  as  small  as  possible,  and  may  vary  between  1/32  and  1/8 
inch,  according  to  the  size  of  the  armature. 

23.  Length  of  Armature  Core. 

The  number  of  wires  that  can  be  placed  in  one  layer  around 
the  armature  circumference,  and  the  depth  of  the  winding 
space,  determine  the  total  number  of  conductors  on  the  arma- 
ture, and  the  latter,  together  with  the  length  of  active  wire, 
gives  the  length  of  the  armature  core. 

a.  Number  of  Wires  per  Layer. 

For  smooth  armatures  the  number  of  wires  per  layer  is  ob- 
tained in  dividing  the  available  core  circumference  by  the 
thickness  of  the  insulated  armature  wire.  If  the  whole  circum- 
ference is  to  be  filled  by  the  winding,  then 


X 


(35) 


§23] 


DIMENSIONS  OF  ARM  A  TURE   CORE 


73 


where  /zw  =  number  of  armature  wires  per  layer; 
d&  =  diameter  of  armature  core,  in  inches; 
d'&  =  width  of  insulated  armature  conductor,  in  inches. 

See  §  24. 

If,  in  the  metric  system,  d&  is  given  in  cm.  and  d'&  in  mm., 
the  above  formula  becomes: 


10  X 


X  7t 


.(36) 


In  case  the  winding  is  to  consist  in  separated  coils,  the  sum 
of  the  separating  spaces  is  to  be  deducted  from  the  armature 
circumference. 

The  value  of  nw  is  to  be  rounded  off  to  the  nearest  lower 
even  and  easily  divisible  number,  and,  in  the  case  of  a  drum 
armature,  allowance  for  division  strips  or  driving  horns  is  to 
be  made  according  to  Table  XVII.  This  table  gives  the 
average  circumferential  space  occupied  by  the  division  strips  in 
drum  armatures  of  different  sizes  and  various  voltages,  in  per 
cent,  of  the  core  circumference.  After  fixing  the  number 
of  armature  divisions,  which  will  be  shown  in  §  25,  this 
table  may  also  be  used  to  determine  the  thickness  of  the 
driving  horns,  which  are  usually  made  of  hard  wood,  or  fibre, 
and  sometimes  of  iron: 

TABLE  XVII.— ALLOWANCE  FOB  DIVISION  STRIPS  IN  DRUM 
ARMATURES. 


DIAMETER  OF  ARMATURE  CORE. 

PERCENTAGE  OP  CORE  CIRCUMFERENCE 
OCCUPIED  BY  DIVISION  STRIPS. 

Inches. 

Centimetres. 

Up  to  300  Volts. 

400  to  750  Volts. 

800to2000Volts. 

Up  to    3 

Up  to    7.5 

12  % 

15  % 

"      6 

"     15 

10 

12 

15  % 

"    12 

"     30 

8 

10 

12 

"    20 

"    50 

7 

9 

10 

"    30 

"     75 

6 

8 

9 

Denoting  one-hundredth  of  these  percentages  by  k^  the  core 
circumference  being  unity,  the  formula  for  the  number  of  wires 
per  layer  in  a  drum  armature  in  English  measure  becomes  : 


9  a 


(37) 


74  DYNAMO-ELECTRIC  MACHINES.  [§23 

In  metric  measure  the  same  value  of  #w  is  obtained  by  multi- 
plying the  numerator  of  (37)  by  10,  thus  deriving  the  metric 
formula  similarly  as  (36)  is  derived  from  (35). 

In  toothed  armatures  the  number  of  wires  in  one  layer  is 
found  from  the  number,  «'c,  and  the  available  width,  b'm  of  the 
slots  by  the  equation: 


(38) 


In  this  formula  the  value  of  b'm  is  to  be  derived  from  the 
actual  width,  bm  of  the  armature  slots  (§  22),  by  deducting 
the  thickness  of  insulation  used  for  lining  their  sides,  data 
for  the  latter  being  given  in  §  24. 

For  calculation  in  metric  system  the  factor  10  is  -to  be  em- 
ployed, as  before. 

b.   Height  of  Winding  Space.     Number  of  Layers. 

In  dividing  the  available  height,  h'M  of  the  winding  space 
by  the  height  d"M  of  the  insulated  armature  conductor,  the 
number  of  layers  of  wire  on  the  armature  is  found: 


«!  =  number  of  layers  of  armature  wire; 
h\  —  available  height  of  winding  space,  in  inches; 
d"a  =  height  of  insulated  armature  conductor,  in  inch. 

The  height  of  the  insulated  armature  conductor,  tf"a,  in  the 
case  of  round  or  square  wire,  is  identical  with  its  width,  $'a. 

If  h&  is  expressed  in  cm.  and  d"&  in  mm.,  the  right-hand  side 
of  (39)  must  be  multiplied  by  10  in  order  to  correct  the  for- 
mula for  the  metric  system. 

The  available  height,  7z'a,  of  the  winding  space  is  obtained 
from  its  total  height,  hM  averages  for  which  are  given  in  Table 
XVIII.  (page  75)  by  deducting  from  1/32  to  1/4  inch  (see  §  24), 
according  to  size  and  voltage  of  machine,  for  the  insulation  of 
the  -armature  core,  insulation  between  the  layers,  thickness  of 
binding  wires,  etc. 

The  nearest  whole  number  is  to  be  substituted  for  the  value 
of  nv 


§23]  DIMENSIONS  OF  ARMATURE   CORE.  75 

TABLE  XVIII.— HEIGHT  OF  WINDING  SPACE  IN  ARMATURES. 


ENGLISH  MEASURE. 

METRIC  MEASURE. 

Height  of  Winding  Space, 
in  inches. 

Height  of  Winding  Space, 
in  centimetres. 

Diameter 
of 

Smooth  Armature 

Diameter 
of 

Smooth  Armature 

Armature, 
in  inches. 

Core. 

Toothed 
Armature 

Armature, 
in  cm. 

Core. 

Toothed 
Armature 

Drum 

Ring 

Core. 

Drum 

Ring 

Core. 

Armature. 

Armature. 

Armature. 

Armature. 

Up  to    2 

.25 

Up  to  5 

.7 

3 

.3 

.  . 

7.5 

.8 

4 

.35 

.20 

10 

.9 

.5 

1.5 

6 

.4 

.225 

H 

15 

.55 

1.75 

8 

.45 

.25 

I 

20 

:  .1 

.6 

2 

10 

.5 

.275 

25 

.2 

.65 

2.25 

12 

.55 

.3 

i 

30 

.35 

.7 

2.5 

15 

.6 

.325 

H 

40 

.5 

.8 

3 

18 

.65 

.35 

li 

50 

.65 

.9 

3.5 

21 

.7 

.375 

if 

60 

.8 

1 

4 

25 

.75 

.4 

i* 

75 

2 

1.2 

4.5 

30 

.8 

.45 

if 

100 

1.4 

5 

40 

.5 

if 

150 

1.6 

5.5 

50 

.55 

l| 

200 

1.8 

6 

60 

.6 

2 

250 

2 

7 

70 

.65 

2i 

300 

2.2 

8 

80 

.  . 

.7 

2i 

400 

2.5 

9 

90 

.75 

2i 

500 

3 

10 

100 

. 

.8 

2f 

125 

.85 

3 

150 

.9 

3i 

200 

1.0 

The    radial    height   taken    up    by  the   armature-binding  in 
smooth  armatures  averages  as  follows : 


Up  to        i  KW 


5 
10 

200 

500 

1,000 

2,000 


.030  inch 

•035  " 

. 040  ' l 

.050  " 

.060  " 

.070  " 

.085  " 

.100  " 


(No.  24 

(     "     22 

B.  &  S.) 

(     "     21 

n      \ 

(      "     17 

(   "    16 

n      \ 

(    "    14 

tt      \ 

(     "     12 

11      ) 

These  figures,  besides  allowing  for  the  binding  wires,  which 
range  from  No.  24  B.  &  S.  (.020")  to  No.  12  B.  &  S.  gauge 
(.080")  respectively,  as  indicated,  include  the  insulation  of.  the 


76  DYNAMO-ELECTRIC  MACHINES.  [§23 

bands,  the  thickness  of  which,  therefore,  varies  from  .010  to 
.020  inch,  according  to  the  size  of  the  armature.  The  bands 
usually  consist  of  from  12  to  25  convolutions  of  phosphor 
bronze  or  steel  wire,  their  width  varying  from  *£  inch  to  2 
inches.  They  are  insulated  from  the  winding  by  strips  of 
mica  from  j^$  to  i  inch  wider  than  themselves,  and  are  placed 
at  distances  apart  equal  to  about  twice  the  width  of  a  band. 

In  straight-tooth  armatures  recesses  are  usually  turned  to 
receive  a  few  light  bands,  while  armatures  with  projecting  teeth 
and  with  perforated  cores  need,  of  course,  no  binding  at  all. 

c.    Total  Number  of  Armature  Conductors.     Length  of  Armature 

Core. 

The  product  of  the  number  of  layers  and  the  number  of 
conductors  per  layer  gives  the  total  number  of  conductors  on 
the  armature;  and  this,  divided  into  the  total  length  of  active 
armature  conductor,  furnishes  the  active  length  of  one  con- 
ductor, that  is,  the  length  of  the  armature  body: 


l    _     12  X  -£a    _  12  X  n&  X  ^  ?        (4o\ 


where  /a  =  length  of  armature  core  parallel  to  pole  faces,  in 

inches; 
Za  =  length  of  active  armature  conductor,  in  feet,  from 

formula  (26); 
nw  =  number  of   wires  per  layer,   from   formula  (35), 

(36),  or  (37),  respectively; 
«!  =  number  of  layers  of  armature  wire,  from  formula 

(38); 

n$  =  number  of  wires  stranded  in  parallel  to  make  up 
one   armature   conductor   of  area   tfa2,   formula 

(30); 

—  -  -  =  total  number  of  conductors  on  armature. 
«i 

In  the  metric  system,  Za  being  expressed  in  metres,  the 
length  /a  is  found  in  centimetres  by  replacing  the  factor  12  in 
(40)  by  100. 

For  preliminary  calculations  an  approximate  value  of  the 


§23J  DIMENSIONS  OF  ARMATURE   CORE.  77 

number  of  conductors,  N&  all  around  the  polefacing  circum- 
ference of  the  armature,  may  be  obtained  by  dividing  the  con- 
ductor area  found  from  formula  (27)  into  the  net  area  of  the 
winding  space.  Taking  .6  of  the  total  area  of  the  winding 
space  as  an  average  for  its  net  area  in  smooth  armatures  witFi 
winding  filling  the  entire  circumference,  we  obtain: 

#w  X  «i  _     ,,.     _  1,000,000  X  .6  X  d&  X  n  X  h& 

~~  ~~~ 


=  1,885,000   x  ^-* (41) 

This  result  is  to  be  correspondingly  reduced  for  windings 
filling  only  part  of  circumference,  or  to  be  multiplied  by 
(i  —  ^),  see  formula  (36),  in  case  of  a  drum  armature,  re- 
spectively. 

In  toothed  armatures  the  average  net  height  of  the  winding 
space  is  about  three-fourths  of  the  total  depth  of  the  slot, 
hence  the  approximate  number  of  armature  conductors: 

»w  X  «i  _     jy     _  1,000,000  X  n'c  X  &'s  X  24^a 
n&  <?a2 

=  750,000  x  HC  X^.2S  x  h& (42) 

In  (41)  and  (42)  the  values  of  d&,  hM  and  b's  are  given  in 
inches,  and  #a2  in  circular  mils. 

For  metric  calculations  formula  (41)  takes  the  form: 

100  X  .6  X  d&  n  X  h& 


mm. 


*.  X 


*;  = 


and  formula  (42)  is  replaced  by: 

„        IPO  X  «;e  X  b  's  X 

c  ~~  (8  Y 

\°&)  mm. 

=  75  X  *'•        :  X 


/,IQ\ 

(43) 


In  (43)  and  (44)  the  dimensions  dM  hM  and  b\  are  expressed 
in  centimetres,  and  (#ft)  mm.  i°  square  millimetres. 


78  DYNAMO-ELECTRIC  MACHINES.  [§24 

24.  Armature  Insulations. 

a.    Thickness  of  Armature  Insulations. 

According  to  the  size  and  the  voltage  of  a  dynamo  the  thick- 
nesses of  the  insulations  in  its  armature  vary  in  very  wide 
limits. 

The  coating  of  the  armature  conductor,  if  single  wire  is  em- 
ployed, usually  is  effected  by  a  double  cotton  covering  ranging 
in  diametral  thickness  from  .012  to  .020  inch  (0.3  to  0.5  mm.), 
according  to  the  size  of  the  wire  and  the  voltage,  see  Table 
XXVI.,  §  28.  If  stranded  cable  is  used  for  winding  the 
armature,  either  bare  or  single  cotton-covered  wire  is  used  to 
make  up  the  cable,  and  the  whole  is  covered  with  two  or  three 
layers  of  cotton.  The  thickness  of  the  single  cotton  insula- 
tion in  this  case  varies  from  .005  to  .010  inch  (0.125  to  °-25  nim.) 
in  diameter.  For  very  thin  wires,  from  No.  20  B.  W.  G.  (.035 
inch  =  0.9  mm.)  down,  a  double  silk  covering  from  .004  to 
.005  inch  (o. i  to  0.125  mm.)  diametral  thickness  is  applied. 

In  case  of  rectangular  or  wedge-shaped  conductors,  accord- 
ing to  their  size  and  to  the  voltage  of  the  machine,  either  a 
double  cotton  covering,  as  with  wires,  is  used,  or  oiled  paper, 
cardboard,  asbestos,  or  mica  is  employed  for  their  enwrapping 
or  separation.  The  thickness  of  the  insulation  in  the  latter 
case  varies  between  .010  and  .0125  inch  (0.25  and  3  mm.)  each 
side,  see  columns  e  of  the  following  Table  XIX. 

Besides  this  coating  of  the  single  conductors,  sometimes — 
particularly  in  high  voltage  machines — one  or  more  sheets  of 
insulating  material  are  employed  to  separate  the  layers  from 
one  another.  The  thickness  of  this  insulation,  for  which  either 
oiled  paper,  rubber  tape,  silk,  or  mica  is  used,  ranges  from 
.004  to  .030  inch  (o. i  to  0.75  mm.),  columns/,  Table  XIX. 

The  insulation  of  the  conductors  from  the  iron  body  in 
smooth  armatures  is  effected  by  serving  the  core  with  one  or 
two  coatings  of  enamel  or  japan  and  then  covering  it  by  either 
oiled  paper,  cardboard,  canvas,  silk,  tape,  sheet  rubber,  cotton 
cloth,  asbestos,  or  mica,  varying  in  radial  thickness  between 
.010  and  .200  inch  (0.25  and  5  mm.),  columns  a,  Table  XIX. 

In  drum  armatures  the  complete  core  insulation,  besides  this 
circumferential  coating,  a,  consists  of  coverings,  by  over  the 
core  edges,  of  core-face  insulations,  <r,  and  of  shaft-insulations, 


§24] 


DIMENSIONS  OF  ARM  A  TURE   CORE. 


79 


d,  all  overlapping  each  other  as  shown  in  Fig.  53.  The  edge 
insulation  is  effected  by  first  covering  the  core  with  layers  of 
oiled  paper,  oiled  muslin,  or  canvas,  then  winding  with  rubber 
tape,  and  finally  adding  a  layer  of  mica  or  asbestos;  according 
to  the  voltage  and  size  of  machine  this  edge  insulation  varies 


Fig.  53. — Core  Insulations  on  Drum  Armature. 

from  .020  to  .250  inch  (0.5  to  6.4  mm.),  see  columns  b,  Table 
XIX.  The  core-face  insulation  is  made  up  of  circular  sheets 
of  oiled  paper,  muslin,  linen,  cardboard,  asbestos,  vulcanized 
fibre,  or  leatheroid,  in  thicknesses  varying  from  .030  to  .400 
inch  (0.75  to  10  mm.),  columns  c,  Table  XIX.  The  shaft- 
insulation,  finally,  usually  consists  of  rubber  tape  in  connection 
with  oiled  paper,  muslin,  or  mica;  its  radial  thickness  ranges 
from  .050  to  .300  inch  (1.25  to  7.5  mm.),  see  columns  d> 


Fig.  54. — Core  Insulation  of  High-Voltage  Drum  Armature. 

Table  XIX.  In  modern  high-voltage  drum  armatures  mica  is 
used  exclusively  for  insulating  the  core,  the  edge-  and  face- 
insulations  being  united  into  the  form  of  flanged  micanite 
discs,  and  micanite  cylinders  or  tubes  being  used  around  the 
circumference  and  over  the  shaft,  see  Fig.  54.  In  this  case  of 
all-mica  insulation  the  thicknesses  of  the  coatings  at  the 
various  parts  of  the  core  can  all  be  made  alike  and  equal  in 
amount  to  that  of  the  circumferential  covering,  columns  a, 
Table  XIX. 


D  YNA  MO-ELE  C  TRIG  MA  CHINE  S. 


[§24 


In  ring  armatures  the  core  insulation,  a,  is  extended  so  as  to 
include  also  the  inner  circumference  and  the  faces  of  the  body 
as  well.  To  prevent  grounding  of  the  winding  at  the  edges, 
their  insulation  is  thickened  by  coatings  inserted  beneath  the 
circumferential  covering.  In  small  rings,  Fig.  55,  the  insula- 


Fig.  55- — Core  Insulations  on  Small  Ring  Armature. 

tion,  #,  usually  is  applied  in  form  of  a  narrow  band,  and  is 
simply  wrapped  around  the  core,  the  reinforcements  at  the 
edges  being  laid  upon  the  core,  as  the  enwrapping  proceeds, 
in  the  shape  of  short  strips  of  oiled  material  or  mica  of  such 
gauge  as  to  make  the  total  thickness  of  insulation  at  the  edges 
equal  to  the  edge-insulation  given  in  columns  b  of  Table  XIX. 
In  large  ring  machines,  Fig.  56,  the  core  faces  are  often  insu- 


Fig.  56. — Core  Insulations  on  Large  Ring  Armature. 

lated  by  means  of  curved  vulcabeston,  pressboard,  or  micanite 
discs,  b^  fitting  over  the  end  rings;  these  discs  are  pressed  or 
molded  in  special  forms,  and  are  of  a  thickness  ranging  from 
.060  to  .250  inch  (1.5  to  6.4  mm.),  see  columns  b,  Table  XIX. 

For  toothed  and  perforated  armatures,  Fig.  57,  the  core-cir- 
cumference insulation  is  carried  out  in  form  of  channels  or 
tubes  of  paper,  or  cardboard,  or  vulcanized  fibre,  fitted  into 
the  grooves,  or,  especially  in  large  toothed-core  machines,  by 


§24] 


DIMENSIONS  OF  ARMATURE    CORE. 


81 


means  of  micanite  troughs  lining  the  bottom  and  the  sides  of 
the  slots.  The  thickness  of  this  lining  ranges  from  .010  to 
.  125  inch  (0.25  to  3  mm.),  proportional  to  the  size  of  the  slots, 


Fig.  57- — Various  Forms  of  Slot  Insulation. 

and  according  to  the  voltage  of  the  dynamo,  columns  e,  Table 
XIX.  The  core  faces  of  toothed  armatures  are  insulated  in  a 
similar  manner  as  those  of  a  smooth  armature.  Fig.  58  shows 


Fig.  58. — Core  Insulation  of  Large  Toothed-Ring  Armature. 

a  well-insulated  armature  core  of  a  large  toothed-ring  machine, 
micanite  troughs  being  used  in  the  slots  and  micanite  caps  over 
the  end  rings. 


82 


D  YNA  MO- ELE C TRIG  MA  CHINES. 


[§24 


gjg 

5'  on   C   rt   ET}S 

B-.E-3  2,g.'f? 


t/i  rt  A  3  U 
C  n  O   tn 

r*3  B-E.- 


>  oo  o  o  in  ^ 


g  a 


Core  Circum- 
ference. 


Core  Edges. 


•:  :  :  liiSsi! 


Core  Faces. 


Shaft  Insula- 
tion. 


OOOOOOO 


n  in 

8iS 


Risllii 


Slot  Lining. 


Insulation 
between 
Layers. 


Core  Circum- 
ference. 


;^-*  O  ( 
oo< 


Core  Edges. 


EEBiSi 


Core  Faces. 


Shaft  Insula- 
tion. 


Slot  Lining. 


OOOOOO< 


I      Insulation 
between 
Layers. 


Core  Circum- 
ference. 


S>«  O' 
O»  O  I 


Core  Edges. 


Core  Faces. 


Shaft  Insula- 
tion. 


OOOOOO 


=  I 


Slot  Lining. 


Insulation 
between 
Layers. 


Core  Circum- 
ference. 


*          Core  Edges. 


Core  Faces. 


Shaft  Insula- 
tion. 


Sisilii 


i-- 1 


Slot  Lining. 


1222- 


S 


Insulation 
between 
Layers. 


§  24]  DIMENSIONS   OF  ARM  A  TURE   CORE.  83 

In  the  preceding  Table  XIX.  (see  page  82)  the  thicknesses 
of  armature  core  insulations  are  compiled  for  machines  of 
various  sizes  and  for  different  voltages. 

b.   Selection  of  Insulating  Material. 

Armature  insulations  must  not  only  possess  high  insulating 
resistance,  but  also  great  disruptive  strength,  that  is,  the 
ability  to  withstand  rupturing  or  puncturing  by  electric  press- 
ure. Besides  these  two  main  properties,  successful  insulating 
materials  must  also  be  perfectly  flexible  and  elastic,  must  be 
non-absorptive,  and  unaffected  by  heat.  Unfortunately  there 
is  no  material  that  in  a  very  high  degree  possesses  all  these 
properties  together,  and,  in  selecting  armature  insulators, 
such  a  material  is  to  be  chosen  in  every  case  which  best  fulfills 
the  particular  conditions,  having  as  its  prominent  property 
that  which  is  most  desired  without  being  objectionable  in 
other  respects. 

Mica  ranks  highest  in  disruptive  strength,  has  a  high  insu- 
lating resistance,  is  non-absorptive  and  unaffected  by  heat, 
but  it  very  easily  breaks  in  bending,  and  therefore,  in  spite  of 
being  the  most  perfect  armature  insulator,  cannot  be  used  in 
places  where  the  insulation  is  required  to  be  flexible. 

^Paraffined  materials  are  distinguished  by  their  enormous 
insulation  resistance,  and  have  a  high  disruptive  strength;  but 
they  cannot  stand  much  bending,  and  are  seriously  affected  by 
heat. 

Rubber  has  good  insulating  qualities,  and  is  extremely  flexi- 
ble, but  is  injured  by  temperatures  above  65°  Centigrade 
(=  150°  Fahr.). 

Insulating  materials  prepared  by  treating  certain  fabrics, 
such  as  cotton,  linen,  silk,  and  paper  with  linseed  oil,  and  oxi- 
dizing the  oil  at  the  proper  temperature  to  expel  any  moisture, 
although  not  being  of  marked  disruptive  strength  or  of  ex- 
tremely high  insulating  resistance,  yet  make  very  satisfactory 
armature  insulation,  as  they  can  be  made  to  possess  all  the 
properties  required  of  a  perfect  insulator  in  a  practically  suffi- 
cient degree.  By  using  pure  linseed  oil,  properly  treated, 
and  by  exercising  special  care  in  preparing  the  surfaces,  a 
comparatively  high  insulation  value,  both  in  resistance  and  in 
disruptive  strength,  can  be  obtained,  while  the  materials  are 


34  DYNAMO-ELECTRIC  MACHINES.  [§24 

perfectly  flexible,  practically  non-absorptive,  and  affected  only 
by  temperatures  far  above  that  which  entirely  destroys  the 
cotton  or  silk  insulation  on  the  armature  wires.  In  using 
these  materials  care  should  be  taken  that  their  surfaces  are 
perfectly  uniform,  for,  if  the  oil  is  not  evenly  distributed,  the 
disruptive  strength  and  the  insulation  resistance  fall  off  con- 
siderably. The  greatest  thickness  of  an  unevenly  coated, 
oil-insulating  material  determines  the  number  of  layers  of  it 
that  can  be  placed  into  a  certain  space,  while  the  smallest 
thickness  determines  the  insulation-value,  which  often  runs 
as  much  as  fifty  per  cent,  below  that  of  an  evenly  covered 
sheet  of  the  average  thickness  if  the  surfaces  were  uniform. 
Oil  insulations  made  of  pure  linseed  oil  are  preferable  to 
those  in  which  the  ordinary  commercial  oil  is  used,  since  to 
give  the  latter  its  oxidizing  properties  certain  metallic  oxides 
are  employed  which,  although  being  classed  as  insulators,  have 
an  insulating  value  far  below  that  of  oil.  With  commercial 
linseed  oil  there  is,  therefore,  never  any  certainty  that  some 
of  these  oxides  may  not  be  held  in  suspension,  but  it  is  essen- 
tial for  a  high  insulation  resistance  that  an  insulating  material 
shall  not  contain  any  other  substance  having  a  lower  insulating 
value  than  itself. 

Micanite,  which  is  made  of  pure  India  sheet  mica  cemented 
together  with  a  cement  of  very  high  resistance,  can  be  molded 
in  any  desired  shape,  or  in  combination  with  certain  other 
materials  can  be  rendered  more  or  less  pliable,  thus  combin- 
ing the  excellent  qualities  of  mica  with  the  property  of  flexi- 
bility, and  making  a  most  perfect  armature  insulating  material. 
Micanite  cloth,  micanite paper,  and  micanite plate  are  varieties  of 
this  material.  The  latter  is  a  combination  of  sheet  mica  with 
pure  gum  or  solution  of  guttapercha,  or  with  a  special  cement, 
the  office  of  the  gum  or  cement  being  to  hold  the  laminae 
together  but  to  allow  them  to  slide  upon  each  other  when  the 
plate  is  bent. 

Vulcanized  fibre  is  comparatively  low  both  in  resistance  and 
in  disruptive  strength,  and  is  seriously  affected  by  exposure  to 
moisture. 

Vulcabeston,  an  insulating  substance  composed  of  asbestos 
and  rubber,  is  not  affected  seriously  by  high  temperatures,  and 
has  the  advantage  that  it  can  be  molded  like  micanite,  but 


§24] 


DIMENSIONS   OF  ARMATURE   CORE. 


TABLE  XX. — RESISTIVITY  AND  SPECIFIC  DISRUPTIVE  STRENGTH.  OF  VARIOUS 
INSULATING  MATERIALS. 


MATERIAL. 

THICKNESS  USED 
FOR  ARMATURE 
INSULATION. 

AVERAGE  RESISTIVITY 
AT  30°  CENT. 

SPECIFIC  DISRUPTIVE 
STRENGTH. 

Limits, 
in  Volts 
per  mil 
Thickness. 

Practical 
Average. 

Megohms 
per  square 
inch-mil. 

Megohms 
per 
cm.2-mm. 

inch. 

mm. 

Volts 
per 
mil. 

Volts 
per 
mm. 

.004-.020 
.008-.025 
.010-.030 
.012-.050 

.005-.012 
.006-.015 

.006-.015 
.012-.020 

.015-.025 
.030-.  075 

.015-.040 

.001-.  125 
.012-.016 
.008-.020 
.005-.012 
.010-.025 
.010-.075 
.010-.015 
.010-.020 

.005-.030 
.004-.006 
.006-.010 
.003-.006 
004  .008 

.1-.5 
.2-.6 
.2S-.75 
.3-1.25 

.125-.3 
.15-.4 

.15-.4 
.3-.5 

.4-.6 
.75-2.0 
1.5-75 
.35-1.0 

.025^3.0 
.3-.4 
.2-.5 
.125-3 
.25-.G 
.25-.2 
.25-.4 
.25-.S 

.125-.75 
.1-.15 
.15-.25 
.075-.  15 
.1-.2 
.125-.25 
.05-.2 
.2S-.5 
.6-2.0 
.35-1.5 
.15-.3 
.025-.065 
.04-.! 
.04-.  125 
.05-.175 
.15-.3 
1.0-2.5 
3.0-100 
3.0-100 
3.0-100 

7 
680* 
850* 
120 

10 
25 

11,800,000 
10 

25 

470 
600 
6 
10,000 
33,000 
310,000  t 
440,000  t 
490,000  £ 
500,000  t 
980,000  § 
620,000  t 
320,000  ** 

650  tt 
1,850  it 
1,600  « 
6 
3 
2 
11,800,000 
180 
100 
3,000,000 
30 
50 
75 
50 
75 
35 
15 
.06  §§ 

1,800 
173.000 
216.000 
31,000 

2,500 
6,400 

3,000,000,000 
2,500 

6,400 
120,000 
150,000 
1,500 
2,540,000 
8,400,000 
79.000.0UO 
112,000,000 
124,000,000 
127,000.000 
250,000.000 
158,000,000 
81,000,000 

165,000 
340,000 
400,000 
1,270 
760 
510 
3,000,000,000 
45,700 
25,400 
760,000,000 
7,600 
12,000 
18,000 
12,000 
18,000 
9,000 
3,800 
15 
75 
150 

100-180 
225-490 
330-500 
150-250 

260-340 
340-370 

380-480 
210-240 

250-300 
150-325 
900-1,300 
'150-250 
750-900 
2,000-^.000 
1     240-490 
175-310 
390-510 
280-390 
940-1,120 
830-1,040 
575-790 

450-650 
550-700 
600-960 
200-275 
190-250 
160-200 
800-1,000 
830-950 
100-420 
350-600 
30-60 
350-565 
500-570 
320-420 
420-510 
240-265 
60-110 
10-25 
5-20 
15-40 

125 

300 
375 
175 

275 
350 

400 
225 

275 
2UO 
1,000 
175 
800 
3,000 
300 
200 
425 
300 
1,000 
900 
600 

500 
600 
700 
225 
200 
175 
900 
850 
150 
400 
40 
475 
525 
375 
450 
250 
75 
15 
10 
20 

5,000 
12,000 
15,000 
7,000 

11,000 
14,000 

16,000 
9,000 

10,000 
8,000 
40,000 
7,000 
32,000 
120,000 
12,000 
8,000 
17,000 
12,000 
40,000 
36,000 
24,000 

20,000 
24,000 
28,000 
9,000 
8,000 
7,000 
36,000 
34,000 
6,000 
16,000 
1,600 
19,000 
21,000 
15.000 
18,000 
10.000 
3,000 
600 
400 
800 

"       oiled         

and  Muslin,  oiled  
Bristol  Board        

Cotton,    Single    Covering    (on 

Cotton,  Single  Covering,  shel- 
lacked         

Cotton,  Single  Covering,  boiled 

Cotton,  Doable  Covering  
Cotton,  Double  Covering,  shel- 
lacked          

Hard  Rubber     

Linseed  Oil,  pure,  oxidized  .... 

Micanite  Cloth  

"     flexible  
Paper 

"     flexible  

Plate 

"     flexible,  "  A  "  il 
"        "B"f 
Oiled  Cloth  (Cotton,  Linen,  or 
Muslin) 

Oiled  Paper,  single  coat  
double  " 

Paper  white  writing 

"      yellow  

.005-.010 
.002-.  008 
.010-.  020 
.025-.075 
.015-.060 
.006-.012 
.001-.0025 
.0015-.004 
.0015-.005 
.002-.007 
.006-.012 
.040-.  100 

Paraffined  Paper  

Parchment  oiled 

Press  Board  

Rubber  Sheet 

Shellacked  Cloth 

Silk,  Single  Covering  (on  wires) 
"      shellacked. 
"    Double      "            

"      shellacked. 
Varnished  Cheese  Cloth  

Vulcabeston 

Wood,  Mahogany  

Pine  

"      Walnut 

*  Insulation  resistance  at  50°  C.  is  about  §, 

at  70°  C.  about  •&,  and  at  100°  C.  about  &  of^that  at  30°  C. 

t    :;           ;;  :;  ;:  ::  » 

li  Mica  Laminae,  put  together  by  solution  of  guttapercha  (Mica  Insulator  Co.). 

IT     "  "          "          "   patent  cement  (Mica  Insulator  Co.). 

**  The  insulating  properties  of  this  material  (one  of  the  products  of  the  Mica  Insulator  Co.)  is  affected  but  very 
little  by  temperature,  its  specific  resistivity  at  50°  C.  being  about  .9,  at  70°  C.  about  .95,  and  at  100°  C.  about  .85  of 
the  average  resistivity  at  30°  C. 

tt  Resistivity  at  50°  C.  is  about  %,  at  70°  C.  about  J£,  and  at  100°  C  about  ^  °f  tnat  at  3°°  C. 

§§  Calculated  from  tests  made  by  Addenbrooke,  see  Munroe  &  Jamieson's  "  Pocket-Book,"  tenth  edition  (1894), 
page  251. 


86  DYNAMO-ELECTRIC  MACHINES,  [§24 

both  its  resistivity  and  its  specific  disruptive  strength  are  very 
small  comparatively. 

The  preceding  Table  XX.  gives  the  insulating  properties  of 
the  various  insulating  materials  commonly  used,  and  is  aver- 
aged from  information  contained  in  writings  by  Steinmetz,1 
and  by  Canfield  and  Robinson,2  from  a  report  by  Herrick 
and  Burke,3  and  from  tests  expressly  made  for  the  purpose. 
The  values  of  the  disruptive  strength  are  those  between  parallel 
surfaces,  and,  since  for  the  same  material  the  break-down  volt- 
age per  mil  varies  with  the  thickness — in  some  cases  decreasing, 
in  others  increasing  (according  to  the  nature  of  the  material), 
as  much  as  50  per  cent,  when  varying  the  thickness  of  the 
sample  from  .005  to  .025  inch — are  averaged  from  tests  with 
different  thicknesses. 

Since  the  insulation  resistance  varies  considerably  with 
temperature4  (see  notes  to  Table  XX.),  and  since  readings 
taken  with  identically  the  same  samples  at  the  same  tempera- 
ture but  at  different  times  showed  large  deviations — presum- 
ably owing  to  differences  in  moisture — the  figures  for  the 
resistivity  have,  chiefly,  a  comparative  value,  but  may  with 
sufficient  accuracy  be  taken  as  averages  for  the  computation 
of  the  insulation  resistance  of  armatures,  commutators,  etc., 
of  dynamo-electric  machines. 


'•  '"'  Note  on  the  Disruptive  Strength  of  Dielectrics,"  paper  read  before  the 
American  Institute  of  Electrical  Engineers  by  Charles  P.  Steinmetz.  Trans- 
actions A.  I.  E.  E.,  vol.  x.  p.  85  (February  21,  1893);  Electrical  Engineer, 
vol.  xv.  p.  342  (April  5,  1893). 

2  "  The  Disruptive   Strength   of   Insulating    Materials,"    engineering  thesis 
by  M.   C.    Canfield   and    F.    Gge.    Robinson,    Columbia   College,    Electrical 
Engineer,  vol.  xvii.  p.  277  (March  28,  1894). 

3  "  Report   on  Tests   of  Insulating   Materials  manufactured  by  The   Mica 
Insulator  Co.,  Schenectady,  N.  Y.,"  by  Albert  B.  Herrick  and  James  Burke, 
electrical  engineers,  New  York,  August  13,  1896. 

4  "  Effect  of    Temperature   on  Insulating  Materials,"    by  Geo.   F.   Sever, 
A.  Monell,  and   C.   L.    Perry,     Transactions  A.  I.  E.  E.,  vol.  xiii.  p.  225 
(May  20,  1896);  Electrical  World,  vol.  xxvii.  p.  642  (May  30,  1896),  vol.  xxviii. 
p.  41  (July  n,  1896);  Electrical  Engineer,  vol.  xxi.  p.  556  (May  27,  1896). 


CHAPTER   V. 

FINAL    CALCULATION    OF    ARMATURE    WINDING. 

25.  Arrangement  of  Armature  Winding. 

By  "arrangement"  of  the  armature  winding  is  understood 
the  grouping  of  the  conductors  into  a  number  of  armature 
coils,  each  containing  a  certain  number  of  turns,  or  convolu- 
tions, of  the  armature  wire,  and  each  one  corresponding  to 
a  division  of  the  collector  or  commutator. 

a.  Number  of  Commutator  Divisions. 

The  E.  M.  F.  generated  by  the  combination  of  a  series  of 
convolutions,  or  by  a  coil,  while  under  the  commutator 
brushes,  is  not  constant,  but  fluctuates  with  the  rate  of  its 
cutting  lines  of  force  in  the  different  positions  during  that 
period.  This  fluctuation  of  the  E.  M.  F.  of  a  dynamo,  con- 
sequently, increases  with  the  angle  which  is  embraced  by  each 
coil  of  the  armature,  and  can  be  mathematically  determined 
from  the  measure  of  this  angle.  This  is  extensively  treated 
in  §  9,  and  Table  I.  contained  therein  shows  that  in  a 
i2-coil  armature,  in  which  the  angle  inclosed  by  each  coil 
is  30°,  the  fluctuations  of  the  E.  M.  F.  amount  to  ±  1.7 
per  cent,  of  the  maximum  E.  M.  F.  generator;  that  in  an 
i8-coil  armature,  in  which  the  coil-angle  is  20°,  they  are  ± 
Y±  per  cent. ;  for  24  divisions,  corresponding  to  an  angle  of  15°, 
.about  ±  YZ  of  i  per  cent. ;  for  36  coils,  embracing  an  angle  of 
10°  each,  ±  f  of  i  percent.;  for  48  divisions  of  7^°  each, 
±  TV  of  i  per  cent. ;  for  90  divisions  with  coil-angle  of  4°,  ± 
Tf  5  of  i  per  cent. ;  and  that  for  a  360  division  commutator, 
finally,  for  which  the  angle  inclosed  by  each  coil  is  i°,  they  are 
reduced  to  but  T^O  of  i  per  cent. 

From  these  figures  it  is  apparent  that  the  fluctuations  be- 
come practically  insignificant,  or  the  potential  of  the  machine 
practically  steady,  if,  for  bipolar  dynamos,  armature  coils 
of  an  angular  breadth  of  less  than  10°,  or  what  amounts 
to  the  same  thing,  if  commutators  with  from  36  divisions 

87 


88 


D  YNA  MO- RLE C TRIG  MA  CHINES. 


[§25 


upward  are  used.  For  low  potential  machines — up  to  300 
volts — it  has  been  found  good  practice  to  provide,  per  pair  of 
armature  circuits,  from  40  to  60  divisions  in  the  commutator. 

For  high  potential  dynamos  the  voltage  itself  determines 
the  number  of  commutator  bars.  For,  in  these,  the  self- 
induction  set  up  in  the  separate  coils,  and  the  sparking  at  the 
commutator  caused  by  the  potential  of  this  self-induction 
between  two  adjacent  commutator  divisions,  are  more  impor- 
tant considerations  than  the  fluctuation  of  the  E.  M.  F. 

No  potential  below  20  volts  is  able  to  maintain  an  arc 
across  even  the  slightest  distance  between  two  copper  points. 
The  potentials  above  this  figure  necessary  to  carry  an  arc 
over  a  certain  distance  depend  upon  the  intensity  of  the  cur- 
rent. In  order  to  maintain,  between  two  copper  conductors, 
an  arc  of  .040  inch  length, — the  usual  thickness  of  the  com- 
mutator insulation  for  high  voltage  machines, — according  to 
actual  experiments  made  by  the  author,  imitating  as  nearly  as 
possible  the  conditions  of  a  commutator,  a  current  of 

100  amperes  takes  20  volts 

50  "  "  21  " 

20  "  "  23  " 

10  "  "  25  " 

5  "  "  30  " 

2  "  "  40  " 

1  "  "  50  " 

From  this  it  can  be  concluded  that,  in  order  to  prevent  the 
commutator  of  a  high  voltage  machine  from  becoming  un- 
necessarily expensive,  allowances  have  to  be  made  as  follows: 

TABLE  XXI. — DIFFERENCES  OF  POTENTIAL  BETWEEN  COMMUTATOR 

DIVISIONS. 


CURRENT  INTENSITY 
PER  ARMATURE  CIRCUIT. 

DIFFERENCE  OF  POTENTIAL 
BETWEEN  COMMUTATOR  DIVISIONS. 

Over  100  amp 
100  to  50 

eres 

lot 

12 

3  20  vc 
21 

.Its 

50 

20 

15 

23 

20 

10 

20 

25 

10 

5 

25 

30 

5 

2 

30 

40 

2 

1 

35 

50 

§25] 


FINAL   CALCULATION  OF    WINDING. 


89 


The  respective  minimum  numbers  of  commutator  divisions, 
consequently,  are: 


For  over  looA.  p. 
"    100  to  50  A. 
"     50  to  20  A. 
•"      20  to  10  A. 
"      10  to    5  A. 
"        5  to    2  A. 
"        2  to    i  A. 

circuit  :  («c)min 

(^c)min 
"          (^c)min 
"          («c)min 
"           («o)mln 
"           («c)mln 
(«c)min 

E  X  2  «'p       £  X  »  p  1 

- 

•(45) 

20                             IO 

E  X  2  n'v       EX  «'p 

21                          10.5 

^  X  2  n'^  _  E  X  n'p 

23                  ii-5 
_  Ex  *n'v  _Exn'v 

25                  I2-5 
^'  X  2  «'p       E  x  *  p 

3°                  T5 
^  X  2  «'p       ^  x  «'p 

40                   20 
^  X  2  «'p        ^  X  «'p 

^o                  2q 

Having  thus  determined  the  minimum  number  of  divisions 
that  can  be  used  in  the  commutator  without  excessive  spark- 
ing, the  actual  number,  ns,  to  be  employed  has  to  be  chosen  by 
comparing  this  value  of  («c)min  with  the  total  number  of  con- 
ductors on  the  armature,  found  by  multiplying  the  rounded 
result  of  equation  (35),  (37)  or  (38),  respectively,  with  that  of 
formula  (39),  and  dividing  the  product  by  the  number,  n&,  of 
armature  wires  stranded  in  parallel. 

b.  Number  of  Convolutions  per  Commutator  Divisions. 
The  number  of  turns,  nM  of  armature  conductors  per  com- 
mutator division,  or  the  number  of  convolutions  in  each 
armature  coil,  is  then  readily  obtained  by  dividing  the  total 
number  of  armature  convolutions  by  the  number  of  coils,  nc. 
The  number  of  armature  convolutions,  in  ring  armatures,  is 
identical  with  the  number  of  armature  conductors,  while  in 
drum  armatures  it  takes  two  conductors  to  make  one  turn, 
and,  therefore,  the  number  of  turns  is  but  one-half  the  number 
of  conductors.  Hence  we  have  for  ring  armatures: 


»c  x  V 


and  for  </ra*»  armatures  or  drum-wound  ring  armatures: 
n&  ~  2  x  nc  X  n* '     


(46) 


(47) 


90  DYNAMO-ELECTRIC  MACHINES.  [§26 

c.  Number  of  Armature  Divisions. 

If  the  armature  is  to  have  spacing  strips,  or  driving  horns, 
the  number  of  the  armature  divisions  for  this  purpose  depends 
upon  the  number  of  armature  coils,  /zc,  the  number  of  turns 
per  armature  coil,  #a,  and  the  number  of  conductors  in 
parallel,  ns. 

In  ordinary  machines  the  number  of  armature  divisions  is 
usually  made  equal  to  the  number  of  coils,  nc,  and  sometimes 
— especially  in  drum  armatures — double  the  number  of  coils, 
2«c,  is  taken.  For  high  current  output  machines  often  a 
greater  number  of  armature  divisions  than  that  given  by  the 
number  of  coils  is  chosen.  In  such  a  case  the  total  number 
of  single  wires,  or  cables,  ;zc  x  n&  x  ^5,  is  to  be  suitably 
arranged  in  groups.  The  number  of  these  groups  is  to  be 
a  multiple  of  the  number  of  coils,  ?/c,  and  since  the  number  of 
turns  per  coil,  7za,  in  high  current  dynamos,  is  usually  =  i,  the 
problem  of  grouping,  in  this  case,  amounts  to  subdividing 
the  number  of  parallel  wires,  n8. 

26.  Radial  Depth  of  Armature  Core.    Density  of  Mag- 
netic Lines  in  Armature  Body, 

Diameter  and  length  of  the  armature  core  being  deter- 
mined, its  proper,  radial  depth  can  be  readily  found  by  the 
cross-section  to  be  provided  for  the  passage  of  the  magnetic 
lines  of  force. 

The  density  of  lines  permitted  per  unit  area  of  armature 
cross-section  is  limited  by  the  heating  of  the  armature  due  to 
hysteresis  and  eddy  current  losses.  The  heat,  generated  by 
either  of  these  causes,  increases  with  the  density  of  the  lines, 
and  with  the  number  of  magnetic  reversals  per  second.  The 
latter  number  is  the  product  of  the  number  of  revolutions  per 
second  and  the  number  of  magnet  poles,  and  therefore  it  is 
obvious  that,  in  order  to  keep  the  temperature  increase  of  the 
armature  in  its  practical  limits,  in  dynamos  where  this  product 
is  great,  larger  specific  sectional  areas  of  the  armature  core 
are  to  be  allowed  than  in  machines  having  a  small  number  of 
magnetic  reversals,  or  a  low  "  frequency,"  as  half  the  number 
of  reversals,  or  the  number  of  complete  magnetic  "  cycles," 
is  called.  The  former — high  frequency — is  the  case  for  high 


26] 


FINAL    CALCULATION  OF    WINDING. 


speed  and  multipolar  dynamos,  the  latter — low  frequency — 
for  low  speed  and  bipolar  ones.  On  the  other  hand,  large 
multipolar  machines  generally  have  well-ventilated  ring  arma- 
tures, and  in  these  an  even  considerably  larger  amount  of  heat 
generated  will  produce  a  smaller  temperature  increase  tharTiif 
drum  armatures  of  equal  output. 

TABLE  XXII. — CORE-DENSITIES  FOR  VARIOUS  KINDS  OP  ARMATURES. 


SPECIES  OP  DYNAMO. 

TYPE  OP 
MACHINE. 

KIND 

OP 

ARMA- 
TURE. 

FLUX  DENSITY  IN  MINIMUM  CROSS- 
SECTION  OP  ARMATURE. 

Lines  per  sq.  inch. 

jr. 

Lines  per  cm.a 
(Ba 

Incandescent  Dy- 
namos; Railway 
Generators;  Ma- 
chines for  Power- 
Transmission  and 
Distribution;  Sta- 
tionary and  Rail- 
way Motors. 

Bi- 
polar 

High 
Speed 

Drum 

50,000  to  70,000 

8,000toll,000 

Ring 

60,000''    80,000 

9,000  "  12,500 

Low 

Speed 

Drum 

60,000"    80,000 

9,000  "  12,500 

Ring 

70,000  "  100,000 

11,000  "  15,500 

Multi- 
polar 

High 
Speed 

Drum 

35,000  "    50,000 

5,500  "    8,000 

Ring 

50,000  "    70,000 

8,000  "  11,000 

Low 

Speed 

Drum 

40,000"    60,000 

6,000  "    9,000 

Ring 

60,000"    80,000 

9,000  "  12,500 

Series  Arc  Lighting 
Dynamos. 

Bi- 
polar 

High 
Speed 

Ring 

110,000  "  130,000 

17,000  "  20,000 

Multi- 
polar 

High 
Speed 

Ring 

100,000"  120,000 

15,500  "  18,500 

Electroplating  and 
Metallurgical  Dy- 
namos. 

Bi- 
polar 

High 
Speed 

Drum 

40,000  "    60,000 

6,000"    9,000 

Ring 
Ring 

50,000  "    70,000 

8,000  "11,000 

Multi- 
polar 

High 
Speed 

35,000  "    50,000 

5,500"    8,000 

Low 

Speed 

Ring 

40,000"    60,000 

6,000"    9,000 

Accumulator 
Charging     Dyna- 
mos; Battery  Mo- 
tors. 

Bi- 
polar 

High 
Speed 

Drum 

35,000"    50,000 

5,500  "    8,000 

Ring 

40,000  "    60,000 

6,000  "    9,000 

Multi- 
polar 

High 
Speed 

Drum 

30,000"    45,000 

4,500"    7,000 

Ring 

35,000  "    50,000 

5,500  "    8,000 

With  dynamos  for  special  purposes  still  other  points  have 
to  be  considered:  In  arc  lighting  dynamos,  in  order  to  keep 


92  DYNAMO-ELECTRIC  MACHINES.  [§26 

the  magnetic  flux  constant  at  varying  load,  it  is  necessary  to 
make  the  magnetic  circuit  insensitive  to  considerable  changes 
in  exciting  power,  and  this  is  achieved  by  working  the  entire 
circuit  at  a  very  high  saturation;  on  the  other  hand,  in 
machines  used  exclusively  for  charging  accumulators,  the 
saturation  of  the  circuit  should  be  very  low,  for  then,  during 
charging,  when  the  counter  E.  M.  F.  of  the  cells  gradually 
rises,  the  voltage  of  the  charging  dynamo  also  rises  automati- 
cally instead  of  remaining  nearly  constant,  as  it  would  do  if 
the  magnetism  were  incapable  of  further  increase.  Again,  in 
dynamos  for  electroplating,  electrotyping,  electrolytic  pre- 
cipitation of  metals  and  for  electro-smelting,  and  in  motors 
driven  by  accumulators  or  primary  batteries,  on  account  of 
the  very  low  terminal-voltage,  the  field  density  in  the  gaps 
must  be  kept  low  (compare  §  18),  and  therefore  a  low 
saturation  through  the  entire  circuit  is  required. 

According  to  these  considerations,  the  values  given  in  Table 
XXII.,  page  91,  for  the  flux-densities  in  the  radial  cross-section 
of  the  armature  core  are  recommended  (see  §  91). 

The  cross-section  of  the  magnetic  circuit  in  the  armature 
core  is  the  product  of  the  net  length  and  the  net  radial 
depth  of  the  core,  and  of  the  number  of  poles;  and  this  prod- 
uct, divided  into  the  total  magnetic  flux  through  the  arma- 
tures, gives  the  density  of  lines  per  unit  area.  In  order  to 
obtain  the  net  radial  depth,  or  breadth  of  the  cross-section 
of  any  armature  core,  therefore,  the  total  armature  flux  is  to 
be  divided  by  the  product  of  the  armature  density,  of  the  net 
length  of  the  body,  and  of  the  number  of  poles: 


X  &"a  X  4 


The  symbols  used  in  this  formula  denote: 
b&  =  radial  depth,  or  breadth  of  cross-section  of  armature 

core,  in  inches; 
$  —  useful  flux,  in  webers,  or  number  of  useful  lines  of  force 

cutting  armature  conductors,  the  calculation  of  which 

is  the  subject  of  §  56. 
i*a  =  flux-density  in  minimum  area  of  armature  core,  in  lines 

per  square  inch,  given  in  Table  XXII. ; 
np  =  number  of  pairs  of  magnet  poles. 


§  26]  FINAL    CALCULA  TION  OF    WINDING.  93 

4  =  length  of  armature  core,  in  inches,  from  formula  (40) ; 
/&2  =  ratio  of  net  iron  section  to  total  cross-section  of  arma- 
ture core,  see  Table  XXIII. 

For  calculation  in  metric  measure  <&"a  is  to  be  repiac-ed-by 
<Ba  (Table  XXII.)  and  4  to  be  expressed  in  centimetres;  for- 
mula (48),  then,  will  furnish  b^  in  centimetres. 

The  constant  k^  depends  upon  the  material,  and  the  manner 
of  building  up,  of  the  armature  core.  In  order  to  prevent 
excessive  losses  and  resulting  heating  of  the  armature  due  to 
eddy  currents  in  the  iron,  it  is  necessary  to  laminate  the  body 
perpendicular  to  the  direction  of  the  active  armature  con- 
ductors. In  case  the  active  pole  faces  embrace  either  the 
outer,  or  the  inner,  or  both  circumferences  of  the  armature, 
the  active  conductors  are  those  parallel  to  the  shaft,  and  the 
lamination  of  the  core  is  to  be  effected  perpendicularly  to 
the  shaft;  while  in  case  of  the  poles  being  at  the  sides  of 
the  armature  (flat  ring  type),  the  active  conductors  run  per- 
pendicular to  the  shaft,  and  the  lamination  is  to  take  place 
parallel  to  the  shaft.  In  case  of  the  polepieces  embracing 
three  sides  of  the  armature  section,  finally,  the  active  con- 
ductors are  partly  parallel  and  partly  perpendicular  to  the 
shaft,  and  the  lamination,  in  consequence,  is  also  to  be  carried 
out  in  both  directions.  The  materials  for  effecting  these 
various  laminations  are  iron  discs,  iron  ribbon,  and  iron  wire, 
respectively.  The  insulation  of  these  laminae,  in  the  majority 
of  machines,  has  been,  and  is  yet,  effected  by  inserting  sheets 
of  thin  paper,  asbestos,  etc.,  between  them,  although  it  has 
been  repeatedly  shown  by  practical  experiments  l  that  such  an 
insulation  is  not  only  entirely  unnecessary,  but,  on  the  con- 
trary, even  disadvantageous.  For,  in  order  not  to  lose  too 
much  of  the  available  sectional  area  of  the  body,  the  lamina- 
tion in  such  armature  is  usually  made  rather  coarse,  but  it  is 
just  the  fineness  of  the  lamination,  and  not  the  thickness  of 
its  insulation,  that  avoids  in  a  higher  degree  the  generation  of 
eddy  currents.  The  oxide  coating  created  by  heating  the 
iron  is  a  very  effective  and  suitable  insulation  of  the  armature 
core  laminae. 

1  Ernst  Schulz,  Elektrotechn.  Zeitschr.,  December  29,  1893.  See  "Iron  in 
Armatures,"  Electrical  World,  vol.  xxiii.  p.  91  (January  20,  1894),  and  p.  248 
(February  24,  1894). 


94 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§27 


In  the  following  Table  XXIII.  values  of  the  ratio  /£2  of  the 
net  to  the  total  core  section  are  given  for  various  thicknesses 
of  the  iron,  and  for  the  different  modes  of  insulation  now  in 
use: 

TABLE  XXIII. — RATIO  OF  NET  IRON  SECTION  TO  TOTAL  CROSS 
SECTION  OF  ARMATURE  CORE. 


MATERIAL 

OF 

THICKNES 

3  OF  IRON. 

INSULATION 

BETWEEN 

VALUE  OF 

ARMATURE  CORK. 

LAMINAE. 

RATIO  #2. 

inch. 

mm. 

.080 

2 

Paper  or  Asbestos 

0.95  to  0.90 

Sheet  Iron 
(Discs  or  Ribbon). 

.040 
.020 
.010 

1 
0.5 
0.25 

"      "  Enamel 

.92    •   .88 
.90    '    .85 

.85    '    .80 

.010 

0.25 

Oxide  Coating 

.95    '    .90 

.080 

2 

Cotton  Covering 

.90    '   .80 

Square  Wire. 

.040 
.020 

1 
0.5 

Enamel  or  Varnish 

.85    •   .75 
.80    '    .70 

.020 

0.5 

Oxide  Coating 

.90    '    .85 

.080 

2 

Cotton  Covering 

.80    •    .70 

Round  Wire. 

.040 
.020 

1 
0.5 

Enamel  or  Varnish 

.75    «    .65 
.70    '   .60 

.020 

0.5 

Oxide  Coating 

.85    '    .80 

In  large  ring  armatures,  for  the  sake  of  ventilation,  air 
spaces  are  provided  in  modern  machines  by  means  of  light 
brass  frames  inserted  in  certain  intervals  between  the  core 
discs.  In  calculating  the  radial  depth,  bu  of  the  body,  the 
sum  of  these  distance-pieces  is  to  be  deducted  from  the  total 
length,  /a,  of  the  core,  the  reduced  length  so  found  being 
used  instead  of  /a  in  formula  (48). 


27.  Total  Length  of  Armature  Conductor. 

The  amount  of  inactive,  or  "dead,"  wire  required  to  join 
the  active  portions  of  the  armature  conductors  into  continuous 
turns  depends  upon  the  shape  of  the  armature,  the  height  of 
the  winding  space,  and  the  manner  of  winding.  In  an  arma- 
ture, for  instance,  having  a  core  section  of  great  length  parallel 
to  the  pole  faces,  and  but  a  small  thickness  perpendicular  to 


§  27]  FINAL   CALCULA  TION  OF    WINDING.  9$ 

the  same,  this  useless  addition  to  the  generating  wire  will  be 
comparatively  small,  while  in  short  armatures  with  great  core 
depth  the  proportion  of  the  dead  to  the  active  length  will  be 
considerably  greater.  Furthermore,  if  two  armatures  of  same 
length,  same  core  diameter,  and  same  radial  depth  have  equal 
lengths  of  active  conductor,  but  are  wound  with  different 
heights  of  the  winding  space,  —  as  will  be  the  case  if  the  one  has 
a  smooth  core  with  winding  covering  the  entire  circumference 
and  the  other  a  toothed  body,  —  then  the  external  diameters, 
and  consequently  the  lengths  necessary  to  join  the  active  con- 
ductors, are  greater  in  the  latter  case,  and  therefore  it  is  evi- 
dent that  the  armature  with  the  higher  winding  space  requires 
a  greater  total  length  of  armature  conductor.  If,  finally,  two 
otherwise  entirely  equivalent  armatures  are  wound  by  different 
systems,  a  considerable  difference  may  be  found  in  the  total 
lengths  of  wire  required  to  produce  equal  lengths  of  active 
conductor. 

a.  Drum  Armatures. 

The  active  length  of  the  armature  conductor  being  known, 
the  simplest  method  of  expressing  its  total  length,  for  a  drum 
armature,  is 

Zt  =  £3xA,     ..............  (49) 


where  Zt  —  total  length  of  armature  conductor  (parallel  wires 

considered  as  one  conductor); 
Za  =  active  length  of  armature  conductor,  from  formula 

(26); 

£3  —  constant,  depending  upon  shape  of  armature  and 

system  of  winding.     See  Table  XXIV. 

The  ratio,  £3,  of  the  total  to  the  active  length  of  the  arma- 
ture conductor,  in  a  drum  armature,  depends  chiefly  upon  the 
ratio  of  length  to  diameter  of  the  armature  core.  In  modern 
machines  the  lengths  of  drum  armatures  usually  vary  between 
one  and  two  diameters;  in  special  designs,  however,  a  value 
as  low  as  0.75  or  as  high  as  2.5  may  be  taken  for  this  ratio. 
The  following  Table  XXIV.  gives  average  values  of  the  con- 
stant £8  for  various  shape-ratios  for  smooth  as  well  as  for 
toothed  drum  armatures: 


DYNAMO-ELECTRIC  MACHINES. 


[$27 


TABLE  XXIV. — RATIO  BETWEEN  TOTAL  AND  ACTIVE  LENGTH  OF  WIRE 
ON  DRUM  ARMATURES. 


RATIO  OF  LENGTH  TO 
DIAMETER  OP 
ARMATURE  CORE. 

'.'*. 

VALUE  OP  ka. 

Smooth  Armature. 

Toothed  Armature. 

0.75 

2.50 

3.10 

0.8 

2.45 

3.05 

0.9 

2.40 

3.00 

1.0 

2.35 

2.95 

1.1 

2.30 

2.90 

1.2 

2.25 

2.85 

1.8 

2.20 

2.80 

1.4 

2.15 

2.75 

1.5 

2.10 

2.70 

1.6 

2.05 

2.65 

1.7 

2.00 

2.60 

1.8 

1.95 

2.55 

1.9 

1.90 

2.50 

2.0 

1.85 

2.45 

2.25 

1.75 

2.35 

2.5 

1.70 

2.25 

Another  form  often  used  for  expressing  the  total  length  of 
wire  on  a  drum  armature  is  indicated  by  the  formula: 


Zt  =  Nc  x  (4 


X  </a)  =  A,  X 


£•  ;  (50) 


Nc  —  total  number  of  conductors  all  around  armature  circum- 
ference; 
k^  =  constant,  depending  upon  system  of  winding. 

This  formula  (50)  has  the  advantage  over  (49)  that  no  special 
table  is  required  for  its  constant,  since  for  a  certain  type  of 
armature,  and  a  certain  system  of  winding,  £4  is  very  nearly 
constant  for  all  sizes  and  shapes.  The  value  of  £4  for  the 
smooth  drum  armatures  considered  in  Table  XXIV.  lies 
between  1.3  and  1.7,  and  as  an  average  1.5  may  be  taken,  thus 
making  the  formula  for  the  total  length  of  conductor  for 
smooth  drum  armatures: 


=  A  X 


Formula   (51),    then,    means  that  the   additional   length   of 
dead  wire  to  every  conductor  of  a  smooth  drum  armature  is 


§27]  FINAL    CALCULATION  OF    WINDING,  97 

one  and  one-half  times  its  core  diameter,  or  that  the  total 
length  of  one  conductor  in  a  smooth  drum  is  equal  to  the 
length  of  the  body  plus  one  and  a  half  times  the  core  diameter. 
The  reason  why  /£4,  even  for  the  same  type  and  same  winding 
method,  has  not  the  same  value  for  all  sizes,  is  that  the  pro- 
portion of  the  core  diameter  to  the  thickness  of  the  armature 
shaft  is  very  much  different  for  different  sizes.  In  a  small 
drum,  for  instance,  the  shaft  takes  up  considerably  much 
more  room  than  in  a  large  one,  and  therefore  the  dead  lengths 
are  comparatively  larger  in  a  small  machine.  In  fact  £4  =  1.5 
gives  too  high  values  for  small  ratios  of  length  to  diameter, 
which  occur  in  large  drums,  while  the  values  found  by  (51)  for 
large  ratios  of  length  to  diameter,  which  are  met  in  small 
armatures,  are  below  those  given  in  Table  XXIV. 

For  /a  :  d&  =  i,  or  */a  :  /a  =  i,   for  instance,  we  obtain,   by 
comparison  of  (49)  with  (50)  and  (51): 

X    '-f-  =  '  +  x-5  X  i  =  2.5, 

i  la. 

while  Table  XXIV.,  which  is  averaged  from  actual  practice, 
gives  /£3  =  2.35  for  this  ratio,  to  which  number  would  corre- 
spond the  small  value  of 

2.35  —  i 


On  the  other  hand,  if  /a :  d&  =  2,  or  dA  :  /a  =  0.5,  we  get: 
£8  =  i  -f  1.5  X  0.5  =  1.75; 

the  table- value  for  £3  is  1.85  for  this  shape-ratio,  and  therefore 
the  high  value  of 

k  =i.85-i  Q 

•5 
would  answer  in  this  case. 

For  toothed-drum  armatures  the  numerical  value  of  k^  in 
the  practical  limits  of  the  ratio  of  shape,  lies  between  1.9  and 
3,  the  average  being  about  2.5;  hence  formula  (50)  for  toothed- 
drum  armatures  becomes: 

Zt  =  Z0x  /i  +2.5  x^);     (53) 


98 


D  YNA  MO-ELECTRIC  MA  CHINES. 


[§27 


that  is  to  say,  the  average  length  to  be  added  to  each  active 
conductor  in  a  toothed-drum  armature  is  two  and  one-half 
times  the  core  diameter  of  the  drum,  or  the  average  dead 
length  in  each  turn  (consisting  of  two  active  conductors)  is 
five  times  the  diameter  at  the  bottom  of  the  slots. 

b.   Ring  Armatures. 

In  a  helically  or  spirally  wound  ring  armature  of  a  core  sec- 
tion of  given  dimensions,  the  ratio  of  the  total  to  the  active 
length  of  the  conductor  depends  upon  the  arrangement  of  the 


Fig.  65. 


Fig.  66. 


Figs.  59  to  66. — Various  Arrangements  of  Field-Magnet  Frame  around 
Ring  Armature. 

field-magnet   frame.      There   are,  altogether,  eight   different 
possibilities  of  arranging  the  poles  around  a  ring  armature; 
these  eight  methods,  however,  can  be  classified  into  but  five 
principally  different  cases,  viz. : 
Case      I.    Polepieces   facing  one   long  armature  surface,  see 

Figs.  59  and  60; 
"       II.  "        two  long  armature  surfaces,  see 

Figs.  6 1  and  62; 
"     III.  "        one  long  and  two  short  armature 

surfaces,  see  Fig.  63; 

"     IV.  "  "        two  long  and  one  short  armature 

surface,  see  Figs.  64  and  65  ; 

"       V  "  "         one  long  and  two  short,  and  part 

of  second  long  surfpce,  see 
Fig.  66. 


§27]  FINAL   CALCULATION  OF    WINDING.  99 

Denoting  with  /a  the  length,  and  with  £a  the  breadth  of  the 
cross-section,  and  assuming  the  winding-height,  hM  to  be  the 
same  all  around  the  section,  we  obtain  the  following  formulae 
for  calculating  the  total  length  of  conductor  on  a  ring 
armature: 

Case      I.  :     Zt  =  -J^-r--^ —   X  A     (53) 


" 


II.:     A*~          -7-  -XX.      ........  (54) 

'a 

ni.:     Zt  =    M4±AL±A5  x  Za      ........  (55) 

/.-fc  •>.'+  Af- 

IV.:     A  =  ,L&±*«)  +  ^  n   X  L&      ........  (56) 


In  these  formulae  /a,  £a,  and  Za  are  known  by  virtue  of  equa- 
tions (40),  (48)  and  (26),  respectively,  and  h&  can  be  taken 
from  Table  XVIII.,  if  the  actual  winding  depth  is  not  already 
known  by  having  previously  determined  the  winding  and  its 
arrangement. 

A  formula  for  Case  V.  is  not  given,  because,  in  the  first 
place,  the  arrangement  shown  in  Fig.  66  is  not  at  all  practical, 
and  the  makers  who  first  introduced  the  same  have  long  since 
discarded  it,  and,  second,  because  the  distance  of  the  internal 
pole  projections  depends  upon  the  construction  and  manner  of 
supporting  of  the  armature  core,  and,  consequently,  cannot  be 
definitely  expressed. 

c.   Drum-  Wound  Ring  Armatures. 

In  modern  ring  armatures  of  the  types  indicated  by  Figs.  59 
and  60,  the  conductors  facing  two  adjacent  poles  of  opposite 
polarity  are  often  connected  in  the  fashion  of  a  bipolar  drum, 
by  completing  their  turns  across  the  end  surfaces  of  the  arma- 
ture body,  thus  converting  the  multipolar  ring  armature  into 
the  combination  of  as  many  bipolar  drum  armatures  as  there 
are  pairs  of  poles  in  the  field  frame  ;  see  §  43.  By  this 
arrangement,  which  is  illustrated  in  Fig.  67,  not  only  a  con- 


100 


DYNAMO-ELECTRIC  MACHINES. 


[§28 


siderable  saving  of  dead  wire  is  experienced,  but  also  the 
exchanging  of  conductors  in  case  of  repair  is  rendered  much 
more  convenient,  especially  when  in  bending  of  the  connection 
strips  the  Eickemeyer  method  is  applied. 

The  total  length  of  the  armature  conductor  can,  in  this  case, 
be  calculated  by  applying,  for  both  smooth  and  toothed  bodies, 
the  above  formula  (51),  replacing  in  the  same  the  core  diam- 
eter, </a,  by  the  chordal  distance  of  two  neighboring  poles, 
measured  from  centre  to  centre  along  the  circumference  of  the 
armature  over  the  winding.  The  formula  for  the  total  length 
of  conductor  on  a  drum-wound  ring  armature,  therefore,  is  (see 
Fig.  67,  page  101): 

i8o°\ 
<4"  X  sin  -j^r  \ 

.5  x-      -£-     -P/x  A    (57) 

Inserting  in  this  formula  the  numerical  value  for  the  size  of 
half  the  pole  angle,  we  obtain  the  following  set  of  formulae  for 
the  various  pole  numbers  that  may  be  used  in  practice: 

TABLE  XXV. — TOTAL  LENGTH  OF  CONDUCTOR  ON  DRUM- WOUND  RING 

ARMATURES. 


,=(. 


NUMBER  OP 
POLES. 

HALF 
POLE-  ANGLE. 
180° 

LENGTH  op 
POLE-CHORD 
(DIAMETER  =  1) 

TOTAL  LENGTH  OP  ARMATURE 
CONDUCTOR  (FORMULA  57). 

4 

45° 

0.707 

Lt  =  (l  +1.161  X~y^ 

x£a 

6 

30 

.500 

0.750 

8 

22^ 

.383 

.574 

10 

18 

.309 

.464 

12 

15 

.259 

.388 

14 

12£ 

.222 

.333 

16 

m 

.195 

.293 

18 

10 

.174 

.261 

20 

9 

.156 

.235 

24 

n 

.131 

.196 

30 

6 

.105 

.157 

28.  Weight  of  Armature  Winding. 

A  copper  wire  of  i  circular  mil 


\ 


7T 


1,000,000 


X  —  square  inch 
4 


§28]  FINAL   CALCULATION  OF    WINDING^ 


area  weighs  .00000303  pound  per  foot  of  length'.; 

conductor  of  tfa2  circular  mils  sectional  area/ 

weight  per  foot  of  .00000303  x  #a2  pound.     And  the  tota.1  Zt 

feet  of  it,  used  in  winding  the  armature,  will  weigh: 

wt&  =  .00000303  X  <V  X  Lt  ;      ......  (58) 

wt&  =  weight  of  bare  armature  winding,  in  pounds; 
#a2  '=  sectional  area  of  armature  conductor,  in  circular  mils, 

from  formula  (27); 
Zt  =  total  length  of  armature  conductor,  in  feet,  formulae  (49) 

to  (57),  respectively. 


Fig.  67. — Face  Connections  of  Drum-Wound  Ring  Armature. 

In  case  of  round  gauge  wires,  the  product  .00000303  x  #a* 
is  contained  in  the  gauge  table  under  the  heading  "  Ibs.  per 
foot,"  and  consequently  the  bare  weight  of  the  winding  is  found 
by  simply  multiplying  the  respective  table-value  by  the  total 
length,  Zt,  and,  eventually,  by  the  number  of  wires,  n§  stranded 
in  parallel. 

If,  in  case  of  heavy  rectangular  or  trapezoidal  armature  bars, 
the  cross-section,  tfa2,  is  given  in  square  inches,  the  numerical 
constant  in  the  above  formula  (58)  should  be  replaced  by  3.858, 
this  being  the  weight  per  foot  of  a  copper  bar  of  i  square  inch 
sectional  area. 

When  the  length  of  the  wire  is  given  in  metres  and  its  sec- 
tional area  in  square  millimetres,  formula  (58)  will  give  the 
weight  of  the  armature-winding  in  kilogrammes,  if  the  factor 
.0089  is  used  as  the  numerical  constant,  8.9  being  the  specific 
gravity  of  copper,  and  .0089,  therefore,  the  weight  in  kilo- 
grammes of  one  metre  of  copper  wire  having  a  cross-section  of 
one  square  millimetre  area. 


,102 


-l&YNAMO-ELECTRIC  MACHINES. 


[§29 


,c  JWljenoStandapd  g&uge  wire  is  to  be  employed  in  winding  the 
arifraxAirey  it4&-aesi«rable  to  know  the  weight  of  the  winding, 
including  its  covering,  particularly  in  the  case  when  insulated 
wire,  such  as  is  obtainable  from  wire  manufacturers,  is  to  be 
used.  This  covered  weight  of  the  winding  can  be  expressed  as 
a  multiple  of  the  bare  weight,  by  the  equation: 

wt'&  =  £5  X  wt*     (59) 

in  which  £5  is  a  constant  depending  upon  the  ratio  of  the  bare 
diameter  of  the  wire,  to  the  thickness  of  its  insulation.  In 


2,H 


Fig.  68. — Armature-Circuits  of  Multipolar  Dynamo. 

Table  XXVI.,  page  103,  these  ratios  and  the  corresponding 
values  of  kb  are  given  for  all  standard  gauge  wires  likely  to  be 
used  for  winding  armatures,  for  single  and  for  double  cotton 
covering. 

29.  Armature  Resistance. 

The  electrical  resistance  of  the  armature  winding  can  be 
determined  by  the  total  length  of  wire  wound  on  the  armature, 
and  from  the  sectional  area  of  the  conductor.  If  R&  denotes 
the  total  resistance  of  the  armature  wire,  all  in  one  continuous 
length,  and  if  there  are  riv  bifurcations  in  the  armature,  and, 
therefore,  2  n'p  electrically  parallel  armature  portions,  then  the 


§29] 


FINAL  CALCULATION   OF    WINDING. 


103 


armature  forms  the  combination  of  2  «'p  parallel  branches  of 

JR. 


ohms 


2  n 


resistance  each. 
TABLE  XXVI. — WEIGHT  OF  INSULATION  ON  ROUND  COPPER  WIRE. 


GAUGE 

OP 

WIRE. 

DIAMETER 

SINGLE  COTTON  INSULATION. 

DOUBLE  COTTON  INSULATION. 

'         O 

. 

OP  WIRE 

. 

OJ               - 

g  :    .£  <D 

C 

*a 

-     8 

2g 

('•RARF^ 

03  g 

^  x>  o 

O  00  "~           ^  e= 

C)   5n   C 

O    02  *> 

"te  c5 

i 

02 

10AJMB/I 

IS      . 

ts  «s  a 

IP 

sill 

Sill 

S  +3  •? 

fl|i 

**"  o~  t> 

£  ° 

fl>  *-*^ 

||| 

3  aj.2 

ojjts 

Ctf-^oly 

||13*S 

i  N" 

« 

CQ 

inch 

mm 

*o 

£3, 

is| 

& 

i   •  'o 

Kjll 

*s| 

^ 

1 

.300 

7.62 

.020 

15 

2.28 

1.0228 

'i 

.289 

7.34 

1     .020 

14.45 

2.32 

1.0232 

'2 

.284 

7.21 

.020 

14.2 

2.33 

1.0233 

3 

.259 

6.58 

.020 

12.95 

2.40 

1.024 

'2 

.258 

6.55 

.020 

12.9 

2.40 

1.024 

'i 

.238 

6.04 

020 

11.9 

2.50 

1.025 

'3 

.229 

5.82 

.020 

11.45 

2.55 

1.0255 

'5 

.220 

5.59 

0-20 

11 

2.65 

1.0265 

'4 

.204 

5.18 

.012 

17 

2.20 

1.022 

.020 

10.2 

2.85 

1.0285 

'e 

.203 

5.16 

.012 

16.9 

2.20 

1.022 

.020 

10.15 

2.86 

1.0286 

.  . 

*5 

.182 

4.62 

.012 

15.15 

2.27 

10227 

.018 

10.1 

2.87 

1.0287 

7 

.180 

4.57 

.012 

15 

2.28 

1.0228 

.018 

10 

2.90 

1.029 

8 

.165 

4.19 

.012 

13.75 

2.33 

1.0233 

.018 

9.17 

3.20 

1.032 

'e 

.162 

4.12 

.010 

16.2 

2.24 

1.0224 

.018 

9 

3.25 

1.0325 

*9 

.148 

3.76 

.010 

14.8 

2.30 

1.023 

.016 

9.25 

3.15 

1.0315 

'7 

.144 

3.66 

.010 

14.4 

232 

1.0232 

.016 

9 

3.25 

1.0325 

io 

.134 

3.40 

.010 

13.4 

2.36 

1.0236 

.016 

8.4 

3.55 

1.0355 

*8 

.1285 

3.27 

.010 

12.85 

2.40 

1.024 

.016 

8 

3.75 

1.0375 

ii 

.120 

3.05 

.010 

12 

2.50 

1.025 

.016 

7.5 

4.10 

1.041 

9 

.1144 

2.91 

.010 

11.4 

2.55 

1.0255 

.016 

7.1 

4.35 

1.0435 

i2 

.109 

2.77 

.010 

10.9 

2.66 

1.0266 

.016 

6.8 

4.60 

1.046 

io 

.102 

2.59 

.010 

10.2 

2.85 

1.0285 

.016 

6.4 

5.00 

1.05 

is 

.095 

2.41 

.010 

9.5 

3.10 

1.031 

.016 

5.9 

5.55 

1.  Oi355 

ii 

.091 

2.31 

.010 

9.1 

3.25 

1.0325 

.016 

5.7 

5.85 

1.0585 

i4 

.083 

2.11 

.007 

12 

2.50 

1.025 

.016 

5.2 

6.60 

1.066 

12 

.081 

2.06 

.007 

11.6 

•2.54 

1.0254 

.016 

5.1 

6.80 

1.068 

15 

13 

.072 

1.83 

.007 

10.3 

2.80 

1.028 

.016 

4.5 

7.80 

1.078 

16 

.065 

:.65 

.007 

9.3 

3.15 

1.0315 

i     .016 

4.1 

8.60 

1.086 

ii 

.064 

.63 

.007 

9.1 

3.25 

1.0325 

.016 

4 

8.80 

1.088 

if 

.058 

1.47 

.007 

8.3 

3.60 

1.036 

.014 

4.1 

8.60 

1.086 

is 

.057 

.45 

.007 

8.1 

3.70 

1.037 

.014 

4.1 

8.60 

1.086 

16 

.051 

1.30 

.007 

7.3 

4.20 

1.042 

.014 

3.6 

9.60 

1.096 

is 

.049 

1.25 

.007 

7 

4.40 

1.044 

.014 

3.5 

9.80 

1.098 

i7 

.045 

.15 

.005 

9 

3.25 

1.0325 

.012 

3.75 

9.30 

1.093 

i9 

.042 

1.07 

.005 

8.4 

3.55 

1.0355 

.012 

3.5 

9.80 

1.098 

is 

.040 

1.02 

.005 

8 

3.75 

1.0375 

.012 

333 

10.10 

1.101 

19 

.036 

0.91 

.005 

7.2 

4.30 

1.043 

.005* 

7.2 

5.60 

1.056 

20 

.035 

0.89 

.005 

7 

4.40 

1.044 

.005* 

6.00 

1.06 

21 

20 

.032 

0.81 

.005 

6.4 

5.00 

1.05 

I     .005* 

6.4 

6.60 

1.066 

22 

21 

.028 

0.71 

.005 

5.6 

6.00 

106 

.004* 

7 

6.00 

1.06 

23 

22 

.025 

0.64 

.005 

5 

7.00 

1.07 

i     .004* 

6.25 

7.00 

1.07 

24 

23 

.022 

0.56 

.005 

4.4 

8.00 

1.08 

.004* 

5.5 

8.00 

1.08 

25 

24 

.020 

0.51 

.005 

4 

8.80 

1.088 

.004* 

5 

8.80 

1.088 

26 

25 

.018    !   0.46 

.005 

3.6 

9.60 

1.096 

.004* 

4.5 

9.60 

1.096 

27 

26 

.016 

0.41 

.005 

3.2 

10.40 

.104 

.004* 

4 

10.40 

1.104 

28 

27 

.014 

0.36 

.005 

2.8 

11.25 

.1125 

.004* 

3.5 

11.25 

1.1125 

29 

28 

.013 

0.33 

.005 

26 

11.65 

.1165 

.004* 

3.25 

11.65 

1.1165 

30 

.012 

0.31 

.005 

2.4      !    12.05 

.1205 

.004* 

3 

12.05 

1.1205 

29 

.011 

0.28 

.005 

2.2      !    12.45 

.1245 

.004* 

2.75 

12.45 

1.1245 

1 

*  Double  silk  :    i   mil   of  silk  insulation  taken  equal   in  weight   to    1.25   mil   of  cotton 
covering. 


104  DYNAMO-ELECTRIC  MACHINES.  [§29 

In  case  of  a  multipolar  dynamo  with  parallel  grouping  the 
number  of  parallel  armature  branches,  2  n'p)  is  equal  to  the  num- 
ber of  poles  2  np,  and  the  resistance  of  each  branch  becomes 


p  p  . 

see  Fig.  68,  page  102. 

The  joint  resistance  of  these  2  n'p  circuits,  that  is,  the  actual 
armature  resistance,  will  consequently  be 


~ 


4   X   (nfp)*  ' 

The  total  resistance,  £&  ,  of  all  the  armature  wire  in  series 
can  be  calculated  from  the  total  length,  Zt,  and  the  sectional 
area,  #a2,  of  the  conductor  by  the  formula 


where  10.5  is  the  resistance,  in  ohms,  at  15.5°  C.  (  =  60° 
Fahr.)  of  a  copper  wire  of  i  circular  mil  sectional  area  and  i 
foot  length,  and  of  a  conductivity  of  about  98  per  cent,  of  that 
of  pure  copper.  The  quotient 


for  commercial  copper,  or 

iQ-32 
<V  J 

for  chemically  pure  copper,  represents  the  resistance  per  foot 
of  the  armature  conductor,  and  can,  for  every  standard  size  of 
wire,  be  taken  from  the  wire  gauge  table. 

Introducing  the  value  of  ft&  into  the  above  equation,  we 
obtain  the  following  formula  for  the  resistance  at  15.5°  C. 
(  =  60°  Fahr.)  of  any  armature  having  a  single  conductor: 


i£5) (60) 


4    X    (npy 

r&   =   resistance  of  armature  winding  at  15.5°   C.,   in  ohms; 
«'p  =  number   of    bifurcations   of   current   in   armature;    for 

special  values  of  n'p  in  the   usual  cases  see  symbols 

of  formula  (24),  §  16; 


§29]  FINAL    CALCULATION  OF    WINDING.  105 

Zt  =  total  length  of  armature  conductor,    in    feet,   formulae 

(49)  to  (57),  respectively; 
d*  —  sectional  area  of  armature  conductor,   in  circular_mils, 

formula  (27). 

In  an  armature,  each  conductor  of  which  consists  of  n&  par- 
allel strands  of  wire  of  6&*  circular  mils  sectional  area,  there 
are  2  n'p  parallel  circuits  of  n§  wires  each,  or  altogether 
2  X  n'p  X  n&  parallel  circuits  of 

ohms 


2  X  0'p  X 
resistance  each;  the  joint  resistance,  therefore,  is 


4  X  (»'p)"  X  ns 

and  since  in  this  case  the  total  resistance  of  the  whole  arma- 
ture wire  in  series  is 

R&  =  Zt  x  ns    X  I  ^~ 


we  obtain  for  the  resistance  at  15.5°  C.  (  =  60°  Fahr.)  of  any 
armature  winding  consisting  of  «$  strands  of  wire  of  #aia  circu- 
lar mils  sectional  area,  the  general  formula 


«''  X 


X  ^  X 


x 

X 


The  resistance  of  a  commercial  copper  wire  of  i  metre 
length  and  i  square  millimetre  sectional  area  being  .017  ohm 
at  15.5°  C.,  the  formula  for  the  armature  resistance  at  15.  5°  C., 
when  dimensions  are  given  in  metric  units,  becomes: 


r 


4   X   «'p2  X    «fi2 


where  Zt  =  total  length  of  armature  conductor,  in  metres; 
n'p  =  number  of  parallel  armature  branches; 
ns  =  number  of  armature  conductors  wound  in  parallel; 


106  DYNAMO-ELECTRIC  MACHINES.  [§29 

(tfajmm2  =  area  of  single  wire,  in  square  millimetres, 
«s  X  (tfa,W  being  equal  to  (tfa)ram2,  as  obtained  from 
formula  (28). 

In  order  to  obtain  the  armature  resistance  at  any  other 
temperature,  higher  than  15.5°  C.,  add  i  percent,  for  every 
2^°  centigrade  over  15.5°.  The  resistance  r&,  at  15.5°  C., 
being  known,  the  armature  resistance  at  0°  Centigrade  con- 
sequently will  be 

<"•>"- 


If  the  temperatures  are  measured  by  the  Fahrenheit  scale,  i 
per  cent,  is  to  be  added  to  the  resistance  for  every  4^° 
over  60°  Fahr.,  and  the  formula  becomes: 


F.  = 


450 


(64) 


In  both  (63)  and  (64),  r&  is  the  resistance  at  15.5°  C.  (  =  60' 
Fahr.)  found  from  formula  (61)  or  (62),  respectively. 


CHAPTER  VI. 

ENERGY    LOSSES    IN    ARMATURE.       RISE    OF    ARMATURE- 
TEMPERATURE. 

30.  Total  Energy  Loss  in  Armature, 

There  are  three  sources  of  energy-dissipation  in  the  arma- 
ture which  cause  a  portion  of  the  energy  generated  to  be 
wasted,  and  which  give  rise  to  injurious  heating  of  the 
armature.  These  sources  are  (i)  overcoming  of  electrical 
resistance  of  armature  winding,  (2)  overcoming  of  magnetic 
resistance  of  iron,  and  (3)  generation  of  electric  currents  in 
the  armature  core.  The  energy  spent  for  the  first  cause,  that 
is,  the  energy  spent  by  the  current  in  overcoming  the  ohmic 
resistance  of  the  conductors,  is  often  called  the  C*R  loss 
(C  =  current,  R  —  resistance),  for  reasons  evident  from 
§  31.  The  energy  consumed  from  the  second  cause,  or 
spent  in  continually  reversing  the  magnetism  of  the  iron  core, 
as  the  armature  revolves  in  the  field,  is  called  the  hysteresis 
loss  (see  §  32),  and  the  energy  spent  from  the  third  cause, 
in  setting  up  useless  currents  in  the  iron  and,  in  a  small 
degree,  also  in  the  armature  conductors,  is  styled  the  eddy 
current  loss,  or  Foucault  current  loss  (see  §  33). 

The  total  energy  transformed  into  heat  in  the  armature  of 
a  dynamo-electric  machine  is  the  sum  of  the  C*R  loss,  of  the 
hysteresis  loss,  and  of  the  eddy  current  loss,  and  can  be 
expressed  by  the  formula: 

A  -  A+  A  +  A,    (65) 

in  which  PA  =  total  watts  absorbed  in  armature; 

P&  =  watts   consumed   by  armature  winding,  form- 
ula (68) ; 

Ph  =  watts  consumed  by  hysteresis,  formula  (73); 
PI  —  watts   consumed   by   eddy    currents,    formula 
(75)- 

107 


io8  DYNAMO-ELECTRIC  MACHINES.  [§31 

31.  Energy  Dissipated  in  Armature  Winding. 

The  energy  required  to  pass  an  electric  current  through 
any  resistance  is  given,  in  watts,  by  the  product  of  the  square 
of  the  current  intensity,  in  amperes,  into  the  resistance, 
in  ohms.  The  energy  absorbed  by  the  armature  winding, 

therefore,  is: 

Pa=  (/')"  X  r'a,      (66) 

where  P&  =  energy  dissipated  in  armature  winding,  in  watts; 

/'    =  total  current  generated  in  armature,  in  amperes; 

r'a  —  resistance  of  armature  winding,  hot,  in  ohms;  see 

formulae  (60)  to  (64),  respectively. 

The  total  current,  /',  in  series-wound  dynamos,  is  identical 
with  the  current  output  I;  in  shunt-  and  compound-wound 
dynamos,  however,  /'  consists  of  the  sum  of  the  external 
current,  and  the  current  necessary  to  excite  the  shunt  mag- 
net winding.  The  amount  of  current  passing  through  the 
shunt  winding  is  the  quotient  of  the  potential  difference,  E, 
at  the  terminals  of  the  machine,  by  the  resistances  of  the  shunt 
circuit,  rm,  that  is  the  sum  of  the  resistance  of  the  shunt 
winding  and  of  the  regulating  rheostat,  in  series  with  the 
shunt  winding. 

For  the  resistance,  r'a,  of  the  armature  winding,  when 
hot, — in  order  to  be  on  the  safe  side  in  determining  the 
armature  losses, — we  will  take  that  at,  say  65.5°  C.  (=  150° 
Fahr.),  or,  according  to  formula  (63),  the  resistance,  ra,  at 
15.5°  C.  (=  60°  Fahr.),  multiplied  by 


( 


1+_*s£r-_!±o  ]  =  1.2. 


The  energy  dissipated  in  overcoming  the  resistance  of  the 
armature  winding,  consequently,  for  shunt-  and  compound- 
dynamos  can  be  obtained  from  the  formula: 

P&=  1.2  X  (l  +    E\  X   r&  ..(67) 


I  =  current-output  of  dynamo,  in  amperes; 
E  —  E.  M.  F.  output  of  dynamo,  in  volts; 
r&  =  resistance  of  armature,   at  15.5°  C.  (=  60°  Fahr.),  in 
ohms; 


§32] 


ENERGY  LOSSES  IN  AXMATUKE. 


109 


rm  =  resistance  of  shunt-circuit  (magnet  resistance  -j-  reg- 
ulating  resistance)  at  15.5°  C.  (for  series  dynamos 


If  P&  is  to  be  computed  before  the  field  calculations  are 
made,  that  is  to  say,  before  rm  is  known,  it  is  sufficiently 
accurate  for  practical  purposes  to  express,  from  experience, 
the  total  armature  current,  /',  as  a  multiple  of  the  current 
output,  I;  and,  therefore,  we  have  approximately 


=  1.2 


X  (k&  X    /)2    X  ra      ........  (68) 

and  in  this  the  coefficient  k6  for  series  dynamos  is  k6  =  i,  and 
for  shunt-  and  compound-wound  dynamos  can  be  taken  from 
the  following  Table  XXVII.: 

TABLE  XXVII.  —  TOTAL  ARMATURE  CURRENT  IN  SHUNT-  AND  COMPOUND- 
WOUND  DYNAMOS. 


CAPACITY 

IN 

KILOWATTS. 

SHUNT  CURRENT 
IN  PER  CENT. 
OP  CURRENT  OUTPUT. 

TOTAL  CURRENT, 
AS  MULTIPLE 
OF  CURRENT  OUTPUT. 

#6 

.1 

15* 

.15 

.25 

12 

.12 

.5 

10 

.10 

1 

8 

.08 

2.5 

7 

.07 

5 

6 

.06 

10 

5 

1.05 

20 

4 

1.04 

30 

3.5 

1.035 

50 

3 

1.03 

100 

2.75 

1.0275 

200 

2.5 

1.025 

300 

2.25 

1.0225 

500 

2 

1.02 

1,000 

1.75 

1.0175 

2,000 

1.5 

1.015 

32.  Energy  Dissipated  by  Hysteresis. 

The  iron  of  the  armature  core  is  subjected  to  successive 
magnetizations  and  demagnetizations.  Owing  to  the  mole- 
cular friction  in  the  iron,  a  lag  in  phase  is  caused  of  the 
effected  magnetization  behind  the  magnetizing  force  that 
produces  it,  and  energy  is  dissipated  during  every  reversal 


no  D  YNA MO- RLE C TRIG  MA  CHINES.  [§32 

of  the  magnetization.  The  name  of  "Hysteresis"  (from  the 
Greek  vGrepico,  to  lag  behind)  was  given  by  Ewing,  in 
1881,  to  this  property  of  paramagnetic  materials,  by  virtue  of 
which  the  magnetizing  and  demagnetizing  effects  lag  behind 
the  causes  that  produce  them. 

Although  Warburg,1  Ewing,2  Hopkinson,3  and  others  have 
made  numerous  researches  about  the  nature  of  this  property 
of  paramagnetic  substances,  it  was  not  until  recently  that  a 
definite  Law  of  Hysteresis  was  established.  In  an  elaborate 
paper  presented  to  the  American  Institute  of  Electrical 
Engineers  on  January  19,  1892,  Charles  Proteus  Steinmetz  * 
gave  the  results  of  his  experiments,  showing  that  the  energy 
dissipated  by  hysteresis  is  proportioned  to  the  i.6th  power 
of  the  magnetic  density,  directly  proportional  to  the  number 
of  magnetic  reversals  and  directly  proportional  to  the  mass  of 
the  iron.  This  law  he  expressed  by  the  empirical  formula: 

p\  =  ih  x  &a6  x  jv;  x  M\9 

where  P\  =  energy  consumed  by  hysteresis,  in  ergs; 

rfl     =  constant  depending  upon  magnetic  hardness  of 

material  ("  Hysteretic  Resistance"); 
(Ba    =  density  of  lines  per  square  centimetre  of  iron; 
N^  —  frequency,  or  number  of  complete  cycles  of   2 

reversals  each,  per  second; 
M\  =  mass  of  iron,  in  cubic  centimetres. 
The  values  of  the  hysteretic  resistance  found  by  Steinmetz 
for    various    kinds  of    iron   are    given    in    Table    XXVIII., 
page  in. 

For  the  materials  employed  in  building  up  the  armature 
core,  according  to  this  table,  we  can  take  the  following  aver- 
age values  of  the  hysteretic  resistance: 

Sheet  iron  :  tjl  —  .0035, 
Iron    wire  :  rfl  —  .040. 


'Warburg,  Wiedem.  Ann.,  vol.  xiii.  p.  141    (1881)  ;    Warburg  and  Hoenig, 
Wiedem.  Ann.,  vol.  xx.  p.  814  (1884). 

2  Ewing,  Proceed.  Royal  Soc.,  vol.  xxxiv.  p.  39,  1882  ;   Philos.  Trans.,  part 
ii.  p.  526  (1885). 

3  J.  Hopkinson,  Philos.  Trans.  Royal  Soc.,  part  ii.  p.  455  (1885). 

4  Steinmetz,    Trans.  A.  I.  E.  E.,    vol.   ix,  p.  3  ;  Electrical  World,  vol.  xix. 
pp.  73  and  89  (1892);  vol.  xx.  p.  285  (1892). 


§32]  ENERGY  LOSSES  IN  ARMATURE.  m 

TABLE  XXVIII. — HYSTERETIC  RESISTANCE  FOR  VARIOUS  KINDS  OF  IRON. 


KIND  or  IRON. 

HYSTERETIC  RESISTANCE. 

Sheet  Iron,  magnetized  lengthwise  

0025  to   005 

0165"  thick  (—   42  mm  ) 

0035 

.015"       "      (—  .38     "    ) 

004 

.006"       "     (—  .15     "    )  

005 

magnetized  across  Lamination  

007 

Iron  Wire  length-magnetization 

0035 

cross-                              ... 

040 

Wrought  Iron,  Norway  Iron  

0023 

"     ordinary  mean  .  . 

0033 

Cast  Iron  ordinary    mean  

013 

containing  -§-  %  Aluminium. 

0137 

0146 

Mitis  Metal  . 

0043 

Tool  Steel  glass  hard  

070 

'  '           oil  hardened  

027 

annealed  

0165 

Cast  Steel  hardened  

012  to  028 

"          annealed  

003  to  009 

Inserting  the  average  values  given  on  page  no  into  Stein- 
metz's  equation,  and  reducing  the  latter  to  our  practical  units, 
we  obtain  for  the  energy  loss  by  hysteresis  in  any  armature 
having  core  built  of  discs  or  ribbon  : 


Ph  =  io-7  X  .0035  X  j      X  ^  X  28,316  X  M 

=  5  x  io-7  x  ®Y-6  x  N!  x  M,     .........  (69) 

and  in  any  armature  with  core  of  iron  wire  : 

Ph  =  5.7  x  io-6  X  <BV  X  ^  X  M,      .........  (70) 

where    Ph    =    energy    absorbed     by    hysteresis,     in    watts  ; 

i  watt  =  io7  ergs  ; 

(B*a  =  density,  in  lines  per  square  inch,  correspond- 
ing to  average  specific  magnetizing  force  of 
armature  core,  see  §  91  ; 

JV 
NI    —    frequency,  in  cycles  per  second,  =  —  -  X  ^p  ; 

N  =   number  of  revs,  per  min.,  «p  =  num- 

ber of  pairs  of  poles  ; 

M   =    mass  of  iron  in  armature  core,  in  cubic  feet; 
i  cu.  ft.  =  28,316  cm.3 


112  D  YNAMO-ELECTRIC  MA  CHINES.  [§32 

The  mass,  in  cubic  feet,  for  both  drum  and  ring  armatures 
with  smooth  core  is  : 

_  d'\    X  n  X  b&  X  4  X   £.  .  m  , 

"7^28 

d'"&  =  mean    diameter    of    armature     core,    in    inches, 

=  ^  -  3a,  see  Fig.  45,  page  58  ; 
l&  =  length  of  armature  core,  in  inches; 
b&  =  radial  depth  of  armature  core,  in  inches; 
£2  =  ratio  of  net  iron  section  to  total  cross-section,  see 

Table  XXL,  §  26; 
1,728  =  multiplier  to  convert  cubic  feet  into  cubic  inches. 

And  for  toothed  and  perforated  armatures  : 


„  _  *  &   -        e    S\)    X    4    X    *.  .  ,„„. 

1,728 

d'"&  —  mean  core-diameter,  in  inches  =  d"&  —  (b&  -{-  ^a),  see 

Fig.  48,  page  65  ; 
n'6  =  number  of  slots; 
S"s  =  sectional  area  of  slots,  in  square  inches. 

Formulae  (69)  and  (70)  can  be  rendered  more  convenient 
for  practical  use  by  uniting  the  terms  5  x  io~7  X  (BY'6  anc^ 
5.7  x  iQ"6  X  ®Y'6>  respectively,  into  one  factor,  77,  the 
factor  of  hysteresis;  that  is,  the  energy  absorbed  by  hysteresis 
in  one  cubic  foot  of  iron,  when  subjected  to  magnetization  and 
demagnetization  at  the  rate  of  one  complete  cycle  (two 
reversals)  per  second. 

For  convenience,  the  author,  in  Table  XXIX.,  has  calcu- 
lated the  numerical  values  of  these  hysteresis  factors,  77,  for 
all  core  densities  from  10,000  to  125,000  lines  per  square  inch, 
thus  simplifying  the  equation  for  the  hysteresis  loss  into  the 
formula: 

Ph  =  77  x  NI  X  M  ............  (73) 

In  Table  XXIX.,  columns  headed  77  -s-  480,  are  added  for 
the  case  the  hysteresis  loss  is  to  be  calculated  for  an  arma- 
ture, of  which  the  weight,  in  pounds,  of  the  iron  core  is  known: 


§32] 


ENERGY  LOSSES  IN  ARMATURE. 


TABLE  XXIX.— HYSTERESIS  FACTORS  FOR  DIFFERENT  CORE 
DENSITIES,  IN  ENGLISH  MEASURE. 


WATTS  DISSIPATED 

WATTS  DISSIPATED 

MAGNETIC 
DENSITY 

AT  A  FREQUENCY  OF  ONE 
COMPLETE  MAGNETIC  CYCLE 
PER  SECOND. 

MAGNETIC 
DENSITY 

AT  A  FREQUENCY  OF  ONE 
COMPLETE  MAGNETIC  CYCLE 
PER  SECOND. 

IN 

IN 

ARMATURE 
CORE. 

Sheet  Iron. 

Iron  Wire. 

ARMATURE 
CORE. 

Sheet  Iron. 

Iron  Wire. 

LINES  OF 

LINES  OF 

FORCE 

FORCE 

PER  SQ.   IN. 

fry  II 
™  a 

per 
cu.  ft. 

per  Ib. 

per 

cu.  ft. 

per  Ib. 

PER  SQ.   IN. 

&"a 

per 
cu.  ft. 

per  Ib. 

per 
cu.  ft. 

per  Ib. 

>? 

rj-f-480 

•n 

Tj+480 

17 

r?-*-480 

•n 

ij+480 

10,000 

1.25 

.0026 

14.3 

.030 

66,000 

25.72 

.0537 

294.0 

.613 

15,000 

2.40 

.0050 

27.4 

.057 

67,000 

26.34 

.0550 

301.0 

.628 

20,000 

3.79 

.0079 

43.3 

.090 

68.000 

26.97 

.0563 

308.2 

.643 

25,000 

5.42 

.0113 

62.0 

.129 

69,000 

27.61 

.0576 

315.5 

.658 

30,000 

7.30 

.0152 

83.5 

.174 

70,000 

28.26 

.0589 

322.8 

.673 

31,000 

7.70 

.0160 

88.0 

.183 

71,000 

28.91 

.0(503 

330.1 

.688 

32,000 

8.10 

.0168 

92.6 

.192 

72,000 

29.56 

.0617 

337.6 

.704 

33,000 

8.50 

.0177 

97.2 

.202 

73,000 

30.22 

.0631 

345.1 

.720 

34,000 

8.91 

.0186 

101.8 

.212 

74,000 

30.89 

.0645 

352.9 

'  .736 

35,000 

9.33 

.0195 

106.5 

.222 

75,000 

31.56 

.0659 

360.7 

.752 

36,000 

9.76 

.0204 

111.5 

.232 

76,000 

32.23 

.0673 

368.5 

.768 

37,000 

10.20 

.0213 

116.5 

.242 

77,000 

32.91 

.0687 

376.3 

.784 

38,000 

10.65 

.0222 

121.6 

.253 

78,000 

33.60 

.0701 

384.2 

.800 

39,000 

11.10 

.0231 

126.8 

.264 

79,000 

34.29 

.0715 

392.1 

.817 

40,000 

11.55 

.0240 

132.0 

.275 

80,000 

34.99 

.0730 

400.0 

.834 

41,000 

12.01 

.0250 

137.2 

.286 

81,000 

3569 

.0745 

408.0 

.851 

42,000 

12.48 

.0260 

142.5 

.297 

82,000 

36.40 

.0760 

416.0 

.868 

43,000 

12.96 

.0270 

148.0 

.308 

as,ooo 

37.11 

.0775 

424.0 

.885 

44,000 

13.45 

.0280 

153.7 

.320 

84,000 

37.82 

.0790 

432.4 

.902 

45,000 

13.95 

.0290 

159.4 

.332 

85,000 

38.54 

.0805 

440.8 

.919 

46,000 

14.45 

.0300 

165.1 

.344 

86.000 

39.27 

.0820 

449.2  |      .936 

47,000 

14.95 

.0311 

170.8 

.356 

87,000 

40.01 

.0835 

457.6        .954 

48.000 

15.45 

.0322 

176.6 

.368 

88,000 

40.75 

.0850 

466  0  !      .972 

49,000 

15.96 

.0333 

182.4 

.380 

89,000 

41.50 

.0865 

474.5        .990 

50,000 

16.48 

.0344 

188.3 

.392 

90,000 

42.25 

.0881 

483.0 

.008 

51,000 

17.01 

.0355 

194.3 

.405 

91,000 

43.00 

.0897 

491  5 

.023 

52,000 

17.55 

.0366 

2006 

.418 

92,000 

4376 

.0913 

500.0 

.042 

53,000 

18.10 

.0377 

206.9 

.431 

93,000 

44.53 

.0929 

509.0 

.064 

54,000 

18.65 

.0388 

213.2 

.444 

94,000 

45.30 

.0945 

518.0 

.0*0 

55,000 

19.21 

.0400 

2195 

.457 

95,000 

46.07 

.0961 

527.0 

.098 

56,000 

19.78 

.0412 

226.0 

.470 

96.000 

46.85 

.0977 

536.0 

.116 

57,000 

20.35 

.0424 

232.6 

.484 

97,000 

47.63 

.0993 

545.0 

.135 

58,000 

20.92 

.0436 

239.2 

.498 

98,000 

48.41 

.1009 

554.0 

.154 

59,000 

21.50 

.0448 

245.8 

.512 

99000 

49.20 

.1025 

5630 

.173 

60,000 

22.09 

.0460 

252.5 

.526 

100,000 

50.00 

.1041 

572.0 

.192 

61,000 

22.69 

.0472 

259.4 

.530 

105,000 

54.06 

.1127 

618.0 

.290 

62,000 

2329 

.0485 

266.3 

.554 

110.000 

58.23 

.1215 

666.0 

1.388 

63,000 

23.89 

.0498 

273.0 

.568 

115,000 

62.53 

.1305 

715.0 

1.490 

64,000 

24.50 

.0511 

280.0 

.583 

120,000 

66.95 

.1400 

765.0 

1.595 

65,000 

25.11 

.0524 

287.0 

.598 

125,000 

71.50 

.1500 

817.5 

1.705 

The  values  of  7;  contained  in  this  table  are  graphically 
represented  in  Fig.  69,  two  different  scales,  one  ten  times  the 
other,  being  used  for  the  ordinates  in  plotting  the  curves,  as 
designated. 

For  the  metric  system,  in  formula  (73)  the  mass  M  in  cubic 


D  YNAMO-ELECTRIC  MA  CHINES.  [§32 

in   cubic   metres,    from    the 

n  c  X  *->s  X  4,  X  #2       c*<L\ 


feet   is   to   be    replaced   by   Ai 
formula: 

M    ^"aXTTX^aX   4X^ 


1,000,000  1,000,000 

the  second  term  of  which  refers  to  toothed  and  perforated 
armatures  only,  and  in  which 

Ml  —  mass  of  iron  in  armature  body,  in  cubic  metres; 
d'"&  =  mean  diameter  of  armature  core,  in  centimetres; 


100 


JJO 


iOO-< 


100 


$-30 


|;20 


FIG.  69. — Hysteresis  Factor  for  Sheet  Iron  and  Iron  Wire,  at  Different  Core 

Densities. 


d'"&  =  d&  —  b& ,  for  smooth  armatures; 

=  d"&  —  (b&  -\-  >^a),  for  toothed  armatures; 
/a  =r  length  of  armature  core,  in  centimetres; 
b&  =  radial  depth  of  armature  core,  in  centimetres; 
n'c  =  number  of  slots; 
6*8  =  slot-area,  in  square  centimetres; 
k9  =  ratio  of  magnetic  to  total   length  of  armature  core, 

Table  XXI.,  §  26. 

Then,  formula  (73)  will  give  the  hysteresis  loss  in  watts,  if 
the  factor  of  hysteresis  ;;  is  replaced  by  rf  from  the  following 
Table  XXX.,  rf  being  calculated  from  3.5  X  io~4  X  (Ba1>6,  in 
case  of  sheet-iron,  and  from  4  x  io~3  X  ($>&'*,  in  case  of  iron 
wire: 


§32] 


ENERGY  LOSSES  IN  ARMATURE. 


TABLE   XXX. — HYSTERESIS  FACTORS  FOR  DIFFERENT  CORE  DENSITIES, 
IN  METRIC  MEASURE. 


1 

;     

WATTS  DISSIPATED 

WATTS  DISSIPATED 

MAGNETIC 
DENSITY 

IN 

AT  A  FREQUENCY  OP 
ONE  COMPLETE  MAGNETIC  CYCLE 
PER  SECOND. 

MAGNETIC 
DENSITY 

IN 

AT  A  FREQUENCY  op 
ONE  COMPLETE  MAGNETIC  CYCLE 
PER  SECOND. 

ARMATURE 

ARMATURE 

CORE. 

CORE. 

LINES  OF 
FORCE 

PER  CM  ^ 

Sheet  Iron. 

Iron  Wire. 

LINES  OF 
FORCE 

Sheet  Iron. 

Iron  Wire. 

(GAUSSES) 

per 

cu.  m. 

per  kg. 

per 
cu.  m. 

per  kg. 

PER  CM. 

(GAUSSES) 

per 
cu.  m. 

per  kg. 

per 

cu.  m. 

per  kg. 

v 

V-i-7,700 

V 

v+r,ro> 

v 

V-i-7,700 

* 

Vn-7,700 

2,000 

67.0 

.0087 

765.1 

.0994 

12,000 

1,177.0 

.1529 

13,451.0 

1.7469 

3,000 

128.1 

.0166 

1,467.1 

.1905 

12,250 

1,216.5 

.1580 

13,902.3 

1.8054 

3,500 

163.9 

.0213 

1,873.1 

.2432 

12,500 

1,256.4 

.1632 

14,359.0 

1.8648 

4,000 

202.9 

.0264 

2,319.3 

.3012 

12,750 

1,296.9 

.1685 

14,821.0 

1.9248 

4,500 

245.0 

.0318 

2,800.2 

.3637 

13,000 

1,337.8 

.1737 

15,288.7 

1.9855 

5,000 

290.0 

.0377 

3,314.6 

.4305 

13,250 

1,379.2 

.1791 

15,7C1.7 

2.0470 

5,250 

313.6 

.0407 

3,583.6 

.4654 

13,500 

1,421.0 

.1845 

16,240.0 

2.1091 

5,500 

337.8 

.0439 

3,860.5 

.5014 

13,750 

1,463.4 

.1901 

16,724.0 

2.1730 

5,750 

362.7 

.0471 

4,145.1 

.5383 

14,000 

1,506.2 

.1952 

17,213.0 

2.2355 

6,000 

388.3 

.0504 

4,437.1 

.5763 

14,250 

1,549.4 

.2012 

17,708.0 

2.2997 

6,250 

414.5 

.0538 

4,848.0 

.6151 

14,500 

1,593.2 

.2069 

18,207.4 

2.3646 

6,500 

441.3 

.0573 

5,043.3 

.6550 

14,750 

1,637.3 

.2126 

18,712.0 

2.4301 

6,750 

468.8 

.0609 

5,357.3 

.6958 

15,000 

1,681.9 

.2179 

19,222.0 

2.4964 

7,000 

496.9 

.0645 

5,678.3 

.7375 

15,250 

1,727.0 

.2243 

19,742.0 

2.5639 

7,250 

525.6 

.0683 

6,006.1 

.7800 

15,500 

1.792.6 

.2302 

20,257.4 

2.6309 

7,500 

554.8 

.0721 

6,355.3 

.8254 

15,750 

1,818.6 

.2362 

20,783.0 

2.6991 

7,750 

584.7 

.0759 

6,682.4 

.8679 

16,000 

1,864.9 

.2422 

21,313.5 

2.7681 

8,000 

615.2 

.0799 

7,030.7 

.9131 

16,250 

1,911.8 

.2484 

21,848.5 

2.8375 

8,250 

646.2 

.0839 

7,385.5 

.9592 

16,500 

1,959.0 

.2544 

22,389.0 

2.9076 

8,500 

677.9 

.0880 

7,747.0 

1.0061 

16,750 

2,006.7 

.2606 

22,934.0 

2.9785 

8,750 

710.1 

.0922 

8,114.8 

1.0539 

17,000 

2,054.9 

.2669 

23,484.5 

3.0499 

9,000 

742.8 

.0965 

8,488.6 

1.1024 

17,250 

2,103.5 

.2732 

24,039.5 

3.1220 

9,250 

776.1 

.1101 

8,869.2 

1.1152 

17,500 

2,152.5 

.2795 

24,599.0 

3.1947 

9,500 

809.9 

.1105 

9,255.6 

1.1202 

17,750 

2,201.9 

.2860 

25,164.0 

3.2681 

9,750 

844.2 

.1110 

9,649.0 

1.2532 

18,000 

2,251.7 

.2924 

25,733.6 

3.3420 

10,000 

879.2 

.1142 

10,047.7 

1.3049 

18,250 

2,301.9 

.2990 

26,307.6 

3.4165 

10,250 

914.6 

.1188 

10,452.2 

1.3574 

18,500 

2,352.6 

.3055 

26,886.0 

3.4918 

10,500 
10,750 

950.5 
987.0 

.1234      10,863.2 
.1282     111,284.0 

1.4108 
1.4650 

18,750 
19,000 

2,403.7 
2,455.1 

.3122 
.3189 

27,470.0 
28,058.6 

3.5676 
3.6440 

11,000 

1,024.0 

.1330 

11,702.5 

1.5198 

19,250 

2,507.1 

.3256 

28,652.0 

3.7210 

11,250 
11,500 

1,061.5 
1,099.5 

.1379      12,131.0 
.1428      12,565.3 

1.5755 
1.6319 

19,500 
19,750 

2,559.3 
2,636.2 

.3324 
.3424 

29,248.6 
29,844.6 

3.7986 
3.8760 

11,750 

1,138.0 

.1478 

13,005.3 

1.6890 

20,000 

2,665.1 

.3461 

30,458.7 

3.9556 

With  regard  to  the  exponent  of  (&"a,  in  formulae  (69)  and 
(70),  Steinmetz's  value,  which  in  the  preceding  is  given  as  1.6 
over  the  whole  range  of  magnetization,  has  been  attacked  by 
Professor  Ewing,1  who  by  recent  investigations  has  found  it  to 
vary  with  the  density  of  magnetization.  In  the  case  of  sheet 


1 J.  A.  Ewing  and  Miss  Helen  G.  Klaassen,  Philos.  Trans.  Roy.  Soc.;  Elec- 
trician (London),  vol.  xxxii.  pp.  636,  668,  713  ;  vol.  xxxiii.  pp.  6,  38  (April  and 
May,  1894);  Electrical  World,  vol.  xxiii.  pp.  569,  573,  614,  680,  714,  740 
(April  and  May,  1894);  Electrical  Engineer,  vol.  xvii.  p.  647  (May  9,  1894). 


n6 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§32 


iron  of  .0185    inch  (  =.47    mm.)   thickness,   for   instance,   the 
hysteretic  exponent  ranged  as  follows: 

TABLE  XXXI. — HYSTERETIC  EXPONENTS  FOR  VARIOUS  MAGNETIZATIONS. 


DENSITY  OF  MAGNETIZATION. 

HYSTEUETIC  EXPONENT. 

Lines  of  Force 
per  Square  Inch. 

&"a 

Linos  per  cm.2 

(.Gausses.) 

&a 

1,300  to    3,000 
3,000  "     6,500 
6,500  "  13,000 
13,000  "  50,000 
50,000  "  90,000 

200  to       500 
500  "    1,000 
1,000  "    2,000 
2,000  "    8,000 
8,000  "  14,000 

1.9 
1.68 
1.55 
1.475 
1.7 

Although  Ewing  thus  has  shown  that  no  formula  with  a 
constant  exponent  can  represent  the  hysteretic  losses  within 
anything  like  the  limits  of  experimental  accuracy,  he  con- 
cludes that  Steinmetz's  exponent  1.6  gives  values  which  are 
nowhere  so  grossly  divergent  from  the  truth  as  to  unfit  them 
for  use  in  practical  calculations.  This  conclusion  holds  par- 
ticularly good  for  the  densities  applied  in  dynamo-electric 
machinery,  as  from  the  above  Table  XXXI.  can  be  seen  that 
for  densities  between  4  and  14  kilogausses  (25,000  and  90,000 
lines  per  square  inch,  respectively),  compare  Table  XXII.,  §  26, 
the  hysteretic  exponent,  according  to  Ewing's  experiments, 
varies  from  1.475  to  I-7>  the  average  of  which  is  1.59,  indeed 
a  good  agreement  with  Steinmetz's  value. 

Experiments  on  the  variation  of  the  hysteretic  loss  per 
cycle  as  function  of  the  temperature  have  been  made  by 
Dr.  W.  Kunz,1  for  the  temperatures  up  to  800°  C.  (  =  1,472° 
Fahr.).  They  show  that  with  rising  temperature  the  hyster- 
esis loss  decreases  according  to  a  law  expressed  by  the  formula 

P\  =  a  +  b  0  , 
where  P'h  =  hysteresis  loss  per  cycle,  in  ergs; 

0  =  temperature,  in  centigrade  degrees; 
a  and  b  =  constants  for  the  material,  depending  upon  the 
temperature  and  on  the    maximal  density  of 
magnetization. 


'Dr.  W.    Kunz,  Elektrotechn.    Zeitschr.,  vol.    xv.  p.    194  (April    5,  1894); 
Electrical  World,  vol.  xxiii.  p.  647  (May  12,  1894). 


§32] 


ENERGY  LOSSES  IN  ARMATURE. 


117 


The  decrease  of  the  hysteretic  loss,  consequently,  consists 
of  two  parts:  one  part,  b  0,  which  is  proportional  to  the  in- 
crease of  the  temperature,  and  another  part,  #,  which  becomes 
permanent,  and  seems  to  be  due  to  a  permanent  change  of  the 
molecular  structure,  produced  by  heating.  This  latter  part, 
in  soft  iron,  is  also  proportional  to  the  temperature,  thus 


10O°  ,2OO°  3OO°  4OO°  5OO°  6OO°  7OO°  8OO°  9OO° 

Fig.   70. — Influence  of  Temperature  upon  Hysteresis  in  Iron  and  Steel. 

making  the  hysteretic  loss  of  soft  iron  a  linear  function  of  the 
temperature,  but  is  irregular  in  steel. 

The  curves  in  the  latter  case  show  a  slightly  ascending  line 
to  about  300°  C.  (  =  572°  Fahr.),  then  change  into  a  rapidly 
descending  straight  portion  to  about  600°  C.  ( =  1,112° 
Fahr.),  when  a  second  "knee"  occurs,  and  the  descension 
becomes  more  gradual. 

The  author  has  refigured  all  of  Kunz's  test  results,  basing  the 
same  upon  the  hysteresis  loss  at  20°  C.  (  =  68°  Fahr.)  as  unity 


n8 


DYNAMO-ELECTRIC  MACHINES. 


[§32 


in  every  set  of  observations.  In  Fig.  70  dotted  lines  have 
then  been  drawn,  inclosing  all  the  values  thus  obtained,  for 
soft  iron  and  for  steel,  respectively,  and  two  full  lines,  one 
for  each  quality  of  iron,  are  placed  centrally  in  the  planes 
bounded  by  the  two  sets  of  dotted  lines,  thus  indicating  the 
average  values  of  the  hysteretic  losses,  in  per  cent,  of  the 
energy  loss  at  20°  C.  Arranging  the  same  in  form  of  a  table, 
the  following  law  is  obtained: 

TABLE  XXXII. — VARIATION  OF  HYSTERESIS  Loss  WITH  TEMPERATURE. 


ENERGY  DISSIPATED  BY  HYSTERESIS  IN  PER 

TEMPERATURE. 

CENT.  OF  HYSTERESIS  Loss  AT  20°  C. 

(=  68°  FAHR.) 

In  Centigrade 
Degrees. 

In  Fahrenheit 
Degrees. 

Soft  Iron. 

Steel. 

20°. 

68° 

100£ 

100£ 

100 

212 

90 

103 

200 

392 

80 

106 

300 

572 

70 

110 

400 

752 

60 

80 

500 

932 

50 

50 

600 

1,112 

40 

20 

700 

1,292 

30 

15 

800 

1,472 

20 

10 

20 

68 

70 

40 

The  last  row  of  this  table,  which  gives  the  hysteresis  loss 
at  20°  C.,  at  the  end  of  the  test,  shows  that  the  energy 
required  to  overcome  the  hysteretic  resistance  is  reduced  to 
about  70  per  cent,  in  case  of  soft  iron  and  to  about  40  per 
cent,  in  case  of  steel,  after  having  been  subjected  to  magnetic 
cycles  at  high  temperatures.  Kunz  further  found  that  the 
hysteretic  energy  loss  can  thus  be  considerably  reduced  by 
repeatedly  applying  high  temperatures  while  iron  is  under 
cyclic  influence. 

For  soft  iron  a  set  of  straight  lines  was  obtained  in  this  way, 
each  following  of  which  had  a  lower  starting  point,  and  de- 
scended less  rapidly  than  the  foregoing  one,  until,  finally, 
after  the  fourth  repetition  of  the  heating  process,  a  stationary 
condition  was  reached. 

For  steel,  already  the  second  set  of  tests  with  the  same 
sample  did  not  show  the  characteristic  form  of  the,  at  first 


§33]  ENERGY  LOSSES  IN  ARMATURE.  119 

ascending,  then  rapidly,  and  finally  slowly  descending  steel 
curve,  but  furnished  a  rapidly  descending  straight  line.  For 
every  further  repetition,  the  corresponding  line  becomes  less 
inclined,  and  for  the  fifth  test  is  parallel  to  the  axiF^of 
abscissae.  Steel,  therefore,  after  heating  it  but  once  as  high 
as  800°  C.  (=  1,472°  Fahr.),  loses  its  characteristic  properties, 
and  with  every  further  repetition  becomes  a  softer,  less  car- 
bonaceous iron. 

33.  Energy  Dissipated  by  Eddy  Currents. 

From  his  experiments  Steinmetz  also  derived  that  the 
energy  consumed  in  setting  up  induced  currents  in  a  body 
of  iron  increases  with  the  square  of  the  magnetic  density, 
with  the  square  of  the  frequency,  and  in  direct  proportion 
with  the  mass  of  the  iron: 

/>',  =  £'    X   (V    X   -AT'   XM'^ 

P'e  —  energy  dissipated  by  eddy  currents,  in  ergs; 
(Bt  =  density  of  lines  of  force,  per  square  centimetre  of  iron; 

N 
TV,  =.  frequency,  in  cycles  per  second,  =  -^—  x  #p; 

M\  =  mass  of  iron,  in  cubic  centimetres; 

f'  —  eddy  current  constant,  depending  upon  the  thickness 
and  the  specific  electric  conductivity  of  the  mate- 
rial; for  the  numerical  value  of  this  constant  Stein- 
metz  gives  the  formula: 


~9 


e'  —  -£-  X  6*  X  y  X  10  -9  =  1.645  X  &  X  y  X  io 

6  =  thickness  of  material,  in  centimetres. 
Y  —  electrical  conductivity,  in  mhos; 
for  iron  :       y  =  100,000  mhos; 
for  copper:  y  =  700,000  mhos. 

Inserting  the  value  of  ef  with  reference  to  iron,  into  the 
above  equation  expressing  the  Eddy  Current  Law,  and  trans- 
forming into  practical  units,  the  eddy  current  loss  in  an  arma- 
ture, in  watts,  is  obtained: 


io-7X  1.645  X(2.54£i)2X  I0~4x5       X-tf/X  28,316 

X  M=  7.22  X  io-8  X  3?  X  (BY   X  N?  X  M.      ..(75) 
i  =  thickness  of  iron  laminae  in  armature  core,  inch; 


120 


DYNAMO-ELECTRIC  MACHINES. 


[§33 


(B"a  =:  density,  in  lines  per  square  inch,  corresponding  to 
average  specific  magnetizing  force  of  armature 
core,  see  §  91; 

N^  --  frequency,  in  cycles  per  second; 
M  =  mass  of  iron,  in  cubic  feet. 

Uniting  again  7.22  x  io~8  X  $?  X  (BV  into  one  factor,  in 
this  case  the  Eddy  Current  Factor,  e,  we  have  the  simplified 
formula: 

Pe  =  e  X^2  XM.      (76) 

TABLE  XXXIII. — EDDY  CURRENT  FACTORS  FOR  DIFFERENT  CORE 
DENSITIES  AND  FOR  VARIOUS  LAMINATIONS,  ENGLISH  MEASURE. 


MAGNETIC 

WATTS  DISSIPATED 

MAGNETIC 

WATTS  DISSIPATED 

DENSITY 

PER  CUBIC  FOOT  OF  IRON 

DENSITY 

PER  CUBIC  FOOT  or  IRON 

IN 

AT  A  FREQUENCY  OP  1  CYCLE 

IN 

AT  A  FREQUENCY  OP  1  CYCLE 

ARMATURE 

PER  SECOND,  e. 

ARMATURE 

PER  SECOND,  e. 

CORE. 

CORE. 

LINES  OP 

LINES  OP 

FORCE 

Thickness  of  Lamination,  Si. 

FORCE 

Thickness  of  Lamination,  Si 

PER  SQ.   IN. 

PER  SQ.   IN. 

«'. 

.010" 

.020' 

.040" 

.080" 

&"a 

.010" 

.020" 

.040" 

.080" 

10,000 

.0007 

.003 

.012 

.046 

66,000 

.0315 

.126 

.503 

2.013 

15.000 

.0016 

.007 

.026 

.104 

67,000 

.0325 

.130 

.519 

2.075 

20,000 

.0029 

.012 

.046 

.185 

68,000 

.0335 

.134 

.534 

2.137 

25,000 

.0045 

.018 

.072 

.288 

69.000 

.0345 

.138 

.550 

2.200 

30,000 

.0065 

.026 

.104 

.416 

70,000 

.0355 

.142 

.566 

2.265 

31,000 

.0070 

.028 

.111 

.444 

71,000 

.0365 

.146 

.582 

2.330 

32,000 

.0074 

.030 

.118 

.472 

72,000 

.0375 

.150 

.599 

2.396 

33,000 

.0079 

.032 

.126 

.503 

73.000 

.0385 

.154 

.616 

2.463 

34,000 

.0084 

.034 

.134 

.534 

74^000 

.0396 

.158 

.633 

2530 

35,000 

.0089 

.036 

.142 

.567 

75,000 

.0407 

.163 

.650 

2.600 

36,000 

.0094 

.038 

.150 

.600 

76,000 

.0418 

.167 

.668 

2.670 

37,000 

.0099 

.040 

.158 

.633 

77.000 

.0429 

.171 

.685 

2.740 

38,000 

.0104 

.042 

.167 

.667 

78,000 

.0440 

.176 

.703 

2.810 

39,000 

.0110 

.044 

.176 

.703 

79,000 

.0451 

.180 

.721 

2.883 

40,000 

.0116 

.046 

.185 

.740 

80,000 

.0462 

.185 

.740 

2.958 

41,000 

.0122 

.049 

.194 

.777 

81,000 

.0474 

.190 

.758 

3.033 

42,000 

.0128 

.051 

.204 

.815 

82,000 

.0486 

.194 

.777 

3.108 

43,000 

.0134 

.054 

.214 

.855 

83,000 

.0498 

.199 

.796 

3.184 

44.000 

.0140 

.056 

.224 

.896 

84,000 

.0510 

.204 

.815 

3.260 

45,000 

.0146 

.059 

.234 

.937 

85,000 

.0523 

.209 

.835 

3.340 

46,000 

.0153 

.061 

.245 

.979 

80,000 

.0535 

.214 

.855 

3.420 

47,000 

.0160 

.064 

.256 

1.022 

87,000 

.0548 

.219 

.875 

3.500 

48.000 

.0167 

.067 

.267 

1.066 

88,000 

.0560 

.224 

.895 

3.580 

49,000 

.0174 

.070 

.278 

1.110 

89,000 

.0573 

.229 

.916 

3.662 

50,000 

.0181 

.072 

.289 

1.155 

90,000 

.0586 

.234 

.937 

3.745 

51,000 

.0188 

.075 

.300 

1.200 

91,000 

.0599       .240 

.958 

3.830 

52000 

.0195 

.078 

.312 

1.248 

92000 

.0612 

.245 

.979 

3.915 

53,000 

.0202 

.081 

.324 

1.297 

93,000 

.0625 

.250 

1.000 

4.000 

54,000 

.0210 

.084 

.337 

1.346 

94,000 

.0638 

.255 

1.021 

4.085 

55,000 

.0218 

.087 

.349 

1.397 

95,000 

.0651 

.261 

1.043 

4.170 

56,000 

.0226 

.091 

.362 

1.448 

96,000 

.0665 

.266 

1.064 

4.257 

57,000 

.0234 

.094 

.375 

1.500 

97,000 

.0679 

.272 

1.086 

4.345 

58.000 

.0242 

.097 

.389 

1.555 

98,000 

.0693 

.277 

1.109 

4.436 

59,000 

.0251 

.101 

.403 

1.610 

99,000 

.0707 

.283 

1.132 

4.528 

60,000 

.0260 

.104 

.416 

1.665 

100,000 

.0722 

.289 

1.156 

4.622 

61,000 

.0269 

.108 

.430 

1.720 

105,000 

.0797 

.319 

1.274 

5.095 

62,000 

.0278 

.111 

.444 

1.776 

110,000 

.0875 

.350 

1.398 

5.593 

63,000 

.0287 

.115 

.458 

1.833 

115,000 

.0955 

.382 

1.528 

6.113 

64,000 

.0296 

.118 

.473 

1.891 

120,000 

.1040 

.416 

1.664 

6.655 

65,000 

.0305 

.122 

.486 

1.951 

125,000 

.1128 

.451 

1.806 

7.222 

1  1  1 

§33] 


ENERGY  LOSSES  IN  ARMATURE. 


121 


The  values  of  e  for  core-densities  from  10,000  to  125,000 
lines  per  square  inch,  and  for  laminations  of  thickness 
tfj  =  .010",  .020",  .040",  and  .080",  are  given  in  the  foregoing 
Table  XXXIII.,  page  120. 

Curves  corresponding  to  the  value  of  £  in  the  above  table 
are  plotted  in  Fig.  71. 


CORE  DENSITY,  IN  LINES  OF  FORCE  P.  SQ<  INCH. 

Fig.  71. — Eddy  Current  Factors  for  Various  Densities  and  Different 
Laminations. 

The  eddy  current  factors  £'  for  the  metric  system,  in  watts 
per  cubic  metre  of  iron,  as  calculated  from  1.645  X  io~7  X 
6'*  X  (Ba2,  for  densities  from  (Ba  =  2,000  to  20,000  gausses, 
and  for  laminations  of  d'{  =  0.25  mm.,  0.5  mm.,  i  mm.,  and 
2  mm.  thickness,  are  given  in  Table  XXXIV.,  page  122. 

Prof.  Thompson1  gives  for  the  calculation  of  the  eddy  cur- 
rent loss  the  following  formula  by  Fleming  which  is  much 
used  by  English  engineers: 

Pe  =  &•  x  &a2  X  N?  X  M\  X  io-16, 

where   Pe  =  eddy  current  loss,  in  watts; 

tf'j  =  thickness  of  iron  laminae,  in  mils; 
(^  =  magnetic  density,  in  lines  per  square  centimetre; 
Nl  —  frequency,  in  cycles  per  second; 
M\  =  mass  of  iron,  in  cubic  centimetres. 


144  Dynamo  Electric  Machinery,"  5th  edition,  p.  137. 


122 


DYNAMO-ELECTRIC  MACHINES. 


[§34 


TABLE  XXXIV. — EDDY  CURRENT  FACTORS  FOR  DIFFERENT  CORE 
DENSITIES  AND  FOR  VARIOUS  LAMINATIONS,  METRIC  MEASURE. 


MAGNETIC 

WATTS  DISSIPATED 

MAGNETIC 

WATTS  DISSIPATED 

DENSITY 

PER  CUBIC  METRE  OF  IRON, 

DENSITY 

PER  CUBIC  METRE  OF  IRON, 

IN 

ATA  FREQUENCY  OF  1  CYCLE 

IN 

AT  A  FREQUENCY  OF  1  CICLE 

ARMATURE 

PER  SECOND,  e'. 

ARMATURE 

PER  SECOND,  e'. 

CORE. 

CORE. 

LINES  OF 
FORCE 

Thickness  of  Lamination,  S'i- 

LINES  OF 
FORCE 

Thickness  of  Lamination,  6'i. 

PER  CM.a 

PER  CM.3 

CQAUSSES) 

(  GAUSSES') 

&a 

0.25mm 

0.5  mm 

1  mm 

2  mm 

<&a 

0.25  mm 

0.5  mm 

1  mm 

2  mm 

2,000 

.041 

.165 

.658 

2.632 

12,000 

1.481 

5.922 

23.688 

94.752 

3,000 

.093 

.370 

1.481 

5.922 

12,250 

1.543 

6.172 

24.687 

98.746 

3,500 

.126 

.504 

2.015 

8.061 

12,500 

1.607 

6.426 

25.704 

102.815 

4,000 

.165 

.658 

2.632 

10.528 

12,750 

1.671 

6.685 

26.741 

106.965 

4,500 

.208 

.833 

3.331 

13.325 

13,000 

1.738 

6.950 

27.801 

111.203 

5,000 

.257 

1.028 

4.113 

16.450 

13,250 

1.805 

7.220 

28.880 

115.520 

5,250 

.283 

1.134 

4.534 

18.136 

13,500 

1.874 

7.495 

29.980 

119.921 

5,500 

.311 

1.244 

4.976 

19.904 

13,750 

1.944 

7.775 

31.100 

124.401 

5,750 

.340 

1.360 

5.441 

21.766 

14,000 

2.015 

8.061 

32.242 

128.968 

6,000 

.370 

1.481 

5.922 

23.689 

14,250 

2.088 

8.351 

33.404 

133.615 

6,250 

.402 

1.607 

6.426      25.704 

14,500 

2.162 

8.647 

34.586 

138.345 

6,500 

.434 

1.738 

6.950 

27.801 

14,750 

2.237 

8.947 

35.789 

143.156 

6,750 

.468 

1.874 

7.495 

29.980 

15,000 

2.313 

9.253 

37.013 

148.050 

7,000 

.504 

2.015 

8.061 

32.242 

15,250 

2.391 

9.564 

38.257 

153.026 

7,250 

.542 

2.167 

8.667 

34.666 

15,500 

2.470 

9.880 

39.521 

158.085 

7,500 

.578 

2.313 

9.253 

37.013 

15,750 

2.550 

10.202 

40.806 

163.225 

7,750 

.619 

2.476 

9.903 

39.613 

16,000 

2.632 

10.528 

42.112 

168.448 

8,000 

.658 

2.632 

10.528 

42.112 

16,250 

2.715 

10.860 

43.438 

173.753. 

8!250 

.700 

2.799 

11.196 

44.785 

16,500 

2.799 

11.196 

44.785 

179.141 

8,500 

.743 

2.971 

11.885 

47.545 

16,750 

2.885 

11.538 

46.153 

184.610 

8,750 

.787 

3.149 

12.595 

50.379 

17,000 

2.971 

11.885 

47.541 

190.162 

9,000 

.833 

3.331 

13.325 

53.298 

17,250 

3.059 

12.237 

48.949 

195.796 

9,250 

.880 

3.519 

14.075 

56.300 

17,500 

3.149 

12.595 

50.378 

201.512 

9,500 

.930 

3.712 

14.846 

59.384 

17,750 

3.239 

12.957 

51.828 

207.311 

9,750 

.977 

3.909 

15.638 

62.550 

18,000 

3.331 

13.325 

53.298 

213.192 

10.000 

1.028 

4.113 

16.450 

65.800 

18,250 

3.424 

13.697 

54.789 

219.155 

10,250 

1.080 

4.321 

17.283 

69.130 

18,500 

3.519 

14.075 

56.300 

225.201 

10.500 

1.134 

4.534 

18.136 

72.545 

18,750 

3.615 

14.458 

57.832 

231.328 

10,750 

1.188 

4.753 

19.011 

76.042 

19,000 

3.712 

14.846 

59.385 

237.538 

11,000 

1.244 

'4.976 

19.905 

79.618 

19,250 

3.810 

15.240 

60.958 

243.830 

11,250 

1.301 

5.205 

20.820 

83.278 

19,500 

3.910 

15.638 

62.551 

250.205 

11,500 

1.360 

5.440 

21.756 

87.022 

19,750 

4.010 

16.041 

64.165 

256.661 

11J50 

1.420 

5.678 

22.712      90.846 

20,000 

4.113 

16.450 

65.800 

263.200 

Transforming  this  formula  into  English  units,  we  obtain: 

*'  X     28'6X  "     X 


=  6.81  X  io~8  X  <V  X  (B 


X 


X 


which  is  practically  the  same  as  formula  (75),  the  results  by 
Fleming's  formula  being  about  5.7  per  cent,  smaller  than  by 
the  former. 

34.  Radiating  Surface  of  Armature. 

The  radiating  surface,  or  cooling  surface,  of  an  armature  is 
that  portion  of  its  superficial  area  which   is  in  direct  contact 


§34] 


ENERGY  LOSSES  IN  ARMATURE. 


123 


with  the  surrounding  air,  and  which  consequently  gives  off  the 
heat  generated  in  the  winding  and  in  the  iron  core.  It  is  evi- 
dent that  the  shape  and  the  construction  of  the  armature 
and  the  arrangement  of  the  field  determine  the  size  of  this 
radiating  portion  of  the  armature  surface.  In  drum  armatures, 
for  instance,  only  the  external  surface  is  liberating  heat,  while 
in  ring  armatures,  according  to  design,  either  the  external 
surface  only  or  any  two  or  three  sides  of  the  cross-section,  or 
even  the  entire  superficial  area  may  act  as  cooling  surface. 

a. — Radiating  Surface  of  Drum  Armatures. 

In  drum  armatures  the  dead  portion  of  the  winding  forms 
two  heads  at  the  ends  of  the  cylindrical  body,  and   the   ex- 


Fig.  72. — External  Dimensions  of  Drum  Armature. 

ternal  area  extending  over  the  cylindrical  part  as  well  as  over 
these  two  conical  heads,  is  the  radiating  surface  of  the  arma- 
ture. In  order  to  calculate  the  cooling  area  of  a  drum  arma- 
ture, it  is  therefore  necessary  to  first  determine  the  size  of 
the  armature  heads. 

The  length  of  the  heads,  /h,  Fig.  72,  depends  upon  the 
diameter  of  the  armature,  the  size  of  the  shaft  and  the  height 
of  the  winding  space,  and  can  be  found  from  the  empirical 
formula: 


4  =  k,  x  d\  +  2  X  ht 


(77) 


where:    /h  —  length  of  armature  heads,  in  inches,  or  in  centi- 
metres; 
£7  =  constant,  depending  upon  the  size  of  the  arma- 

mature  (see  Table  XXXV.); 
d"&  =  external  diameter  of  armature,  in  inches,  or  in 

centimetres; 

h&  =  height  of  winding  space,  in  inches,  or  in  centi- 
metres. 


I24 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§34 


If  </''aand  k&  are  given  in  inches,  (77)  gives  the  length  of  the 
heads  in  inches;  and  if  both  d"&  and  h&  are  expressed  in  centi- 
metres, also  /h  will  be  obtained  in  centimetres. 

The  coefficient  >£7  in  this  formula  varies  with  the  slope  of  the 
head,  and  this,  in  turn,  depends  upon  the  ratio  between  the 
diameter  of  the  armature  and  the  thickness  of  the  shaft.  For, 
in  large  machines  the  shaft  bears  a  smaller  proportion  to  the 
armature  diameter  than  in  small  ones,  and  therefore  in  large 
armatures  there  is  comparatively  much  more  room  between 
the  shaft  circumference  and  the  core  periphery  than  in  small 
armatures,  and  since  the  diameter  of  the  head  must  never 
exceed  that  of  the  armature  itself,  it  is  evident  that  the  slope 
of  the  head  is  smaller,  and  consequently  its  relative  length  is 
larger  in  the  smaller  armatures.  The  following  Table  XXXV. 
gives  the  values  of  this  coefficient  for  the  various  sizes  of 
drum  armatures: 

TABLE   XXXV. — LENGTH  OP  HEADS   IN  DRUM  ARMATURES. 


EXTERNAL  DIAMETER 

OF  ARMATURE. 

d"& 

VALUE 

OF 

AVERAGE  LENGTH 

k, 

OF 

HEADS. 

Inches. 

Cm. 

Up  to    6 

Up  to  15 

.60  to 

.50 

lh  =  .55 

Xrf"a+27*a 

"      12 

"      30 

.55  to 

.45 

=  .50 

X  d\+%h& 

"     18 

"      45 

.50  to 

.40 

—  .   45 

"     24 

"      60 

.45  to 

.35 

=  .40 

X  d\-\-  27ia 

"     30 

"      75 

.40  to 

.30 

=  .35 

X  d\+  2  7>a 

As  to  the  diameters  at  the  ends  of  the  heads,  that  of  the 
front  head,  <4,  at  commutator  end  of  armature,  is  generally 
made  from  0.75  d\  to  i.o  a" ^  while  the  diameter  of  the  end 
washer  of  the  back  head,  ^'h,  ranges  in  size  from  0.5  d"&  to 
°-75  d"v  Taking  dh  —  0.9  d\  as  the  average  diameter  of  the 
front  head,  and  d\  =0.6  a"&  as  that  on  the  back  head  (Figs.  73 
and  74,  page  125),  we  obtain  the  following  formula  for  the 
radiating  surface  of  a  drum  armature: 


SA  =  d\  x 


X 


§34] 


ENERGY  LOSSES  IN  ARMATURE. 


125 


or  approximately: 

SA  =  d\  x  n  x  (4  +  1.8  X  4);     (78) 

SA  —  radiating  surface  of  armature,  in  square  inches^  or^in 

square  centimetres; 

d\  •=.  external  diameter  of  armature,   in  inches,  or   in  centi- 
metres, =  </a  -f  2  h&  ; 
/a  =  length  of  armature  body,  in  inches,  or  in  centimetres, 

formula  (40) ; 

4  =  length  of  armature  head,  in  inches,  or  centimetres;  from 
formula  (77)  and  Table  XXXV. 


ve 

—  Y.3? 

1 

1 

\ 

? 

~"t 

v-*? 

1 

Figs.  73  and  74. — Size  of  Heads  in  Drum  Armatures. 

b. — Radiating  Surface  of  Ring  Armature. 

In  ring  armatures  the  construction  and  mounting  of  the  core 
may  be  such  that  either  one,  two,  or  three,  or  all  four  sides  of 
the  cross-section  are  in  contact  with  the  air,  but  in  modern 


Fig.  75- — Dimensions  of  Ring  Armature. 

machines  almost  without  exception,  all  four,  or  at  least  three 
of  the  surfaces  constituting  the  ring  are  radiating  areas. 

Fig.  75  shows  the  cross-section  of  a  ring  armature. 

In  the  first  mentioned  case  (four  sides)  we  have  the  formula: 

5A  =  2  x  </'".  X  n  x  (4  +  ^  +  4  X  //a),      . .  (79) 


126  DYNAMO-ELECTRIC  MACHINES.  [§35 

and  in  the  latter  case  (three  sides): 
SA  =  d\  x  7t  X  (4  +  2  h^ 

+  2    X    </'"»    X    71    X    fa  +    2  //a);         (80) 

5A  —  radiating  surface  of  armature,  in  square  inches,  or  in 
square  centimetres; 

d' \  =  external  diameter  of  armature,  in  inches,    or  in   centi- 
metres; 

d'"&  =  mean  diameter  of  armature  core,  in  inches,  or  in  centi- 
metres; 

4  =  length  of  armature  core,  in  inches,  or  in  centimetres; 

b&  =  radial  depth  of  armature   core,  in  inches,   or  in  centi- 
metres; 

/i&  =  height  of  winding  space,  in  inches,  or  in  centimetres. 

35.    Specific  Energy  Loss.    Rise  of  Armature  Temper- 
ature. 

While  the  amount  of  the  total  energy  consumed,  PM  formula 
(65),  determines  directly  the  quantity  of  heat  generated  in  the 
armature,  the  amount  of  heat  liberated  from  it  depends  upon 
the  size  of  its  radiating  surface,  upon  its  circumferential 
velocity,  and  upon  the  ratio  of  the  pole  area  to  the  radiating 
surface. 

The  most  important  of  these  factors  in  the  heat  conduction 
from  an  armature  naturally  is  the  size  of  the  radiating  surface, 
while  the  speed  and  the  ratio  of  polar  embrace  are  of  minor 
influence  only;  and  it  is,  therefore,  the  ratio  of  the  energy 
consumed  in  the  armature  to  the  size  of  the  cooling  surface, 
that  is,  the  specific  energy  loss,  which  limits  the  proportion  of 
heat  generated  to  heat  radiated,  and  which  consequently 
affords  a  measure  for  the  degree  of  the  temperature  increase 
of  the  armature. 

A.  H.  and  C.  E.  Timmermann,1  of  Cornell  University,  who 
made  the  armature  radiation  the  subject  of  their  paper  read 
before  the  American  Institute  of  Electrical  Engineers,  in  May, 
1893,  from  a  series  of  elaborate  experiments  drew  the  follow- 
ing conclusions: 

(i)  An  increase  of  the  temperature  of  the  armature  causes 
an  increased  radiation  of  heat  per  degree  rise  in  tempera- 

1  A.  H.  and  C.  E.  Timmermann,  Transactions  Am.  Inst.  of  Elec.  Eng.,  vol. 
x.  p.  336  (1893). 


§35] 


ENERGY  LOSSES  IN  ARMATURE. 


127 


ture,  but  the  ratio  of  increase  diminishes  as  the  temperature 
increases,  and  an  increase  of  the  amount  of  heat  generated  in 
the  armature  increases  the  temperature  of  the  armature,  but 
less  than  proportionately. 

(2)  As  the  peripheral  velocity  is  increased,  the  amount  of 
heat  liberated  per  degree  rise  in  temperature  is  increased,  but 
the  rate  of  increase  becomes  less  with  the  higher  speeds. 

(3)  The  effect  of  the  field-poles  is  to  prevent  the  radiation  of 
heat;  as  the  percentage  of  the  polar  embrace  is  increased,  the 
amount   of   heat   radiated    per   degree    rise    in    temperature 
becomes  less. 

Combining  these  results  with  the  data  and  tests  of  various 
dynamos,  the  author  finds  the  following  values,  given  in  Table 
XXXVI.,  of  the  temperature  increase  per  unit  of  specific  energy 
loss,  that  is,  for  every  watt  of  energy  dissipated  per  square 
inch  of  radiating  surface,  under  various  conditions  of  periph- 
eral velocity  and  polar  embrace: 

TABLE  XXXVI.— SPECIFIC  TEMPERATURE  INCREASE  IN  ARMATURES. 


PERIPHERAL 
VELOCITY. 

RISK  OP  TEMPERATURE  PER  UNIT  OP  SPECIFIC  ENERGY  Loss, 
IN  DEGREES  CENTIGRADE,  Q'&. 

Ratio  of  Pole  Area  to  Total  Radiating  Surface. 

Feet 
per  sec. 

Metres 
per  sec.    \ 

.8 

.7 

100° 
74 
61 
53 
48| 
47 
46 
45 
44 

.6 

95° 

70 
58 
51 
47 
46 
45 
44 
43 

.5 

.4 

.3 

.2 

0 
10 
20 
30 
40 
50 
75 
100 
150 

0 
3 
6 
9 
12 
15 
22.5 
30 
45 

110° 
80 
64 
55 
50 
48 
47 
46 
45 

90° 
67 
56 
49£ 
46 
45 
44 
43 
42 

86° 
64 
54 
48 
45 
44 
43 
42 
41 

83° 
62 
52 
46i 
44 
43 
42 
41 
40 

80° 
60 
50 
45 
43 
42 
41 
40 
40 

In  Fig.  76  these  temperatures  are  represented  graphically; 
Curves  I.,  II.  .  .  VII.,  corresponding  to  Columns  2,  3  ... 
8,  of  Table  XXXVI.  respectively. 

Multiplying  this  specific  temperature  increase  by  the  respec- 
tive specific  energy  loss,  the  rise  of  temperature  can  be  found 
from: 

9.  =  6'aXfi (81) 


128 


D  YNA  MO-ELE  C TRIG  MA  CHINES. 


[§35 


where  0a  =  rise  of  temperature  in  armature,  in  degrees  Centi- 
grade; 

0a  =  specific  temperature  increase,  or  rise  of  armature 
temperature,  per  unit  of  specific  energy  loss,  from 
Table  XXXVI.,  or  Fig.  76; 


30  10  50  60  70 

PERIPHERAL  VELOCITY,  IN  FEET  P.  SEC. 


Fig.  76.  —  Specific  Temperature  Increase  in  Armatures. 

P^  •=.  total    energy   consumed    in    armature,    in    watts, 

formula  (65); 
Sh  =  radiating   surface   of  armature,   in   square  inches, 

from  formula  (78),  (79),  or  (80),  respectively; 
p 
—^  —  specific  energy  loss;   /'.    <?.,   watts  energy  loss  per 

^A 

square  inch  of  radiating  surface. 

In  order  to  obtain  the  temperature  increase  in  Fahrenheit 
degrees,  the  result  obtained  by  (81)  is  to  be  multiplied  by 


§  36J  ENERGY  LOSSES  IN  ARMATURE.  129 

and  if  S^  is  expressed  in  square  centimetres,  the  factor  6.45  must 
be  adjoined. 

36.  Empirical  Formula  for  Heating  of  Drum  Armatures. 

From  tests  made  with  drum  armatures,  Ernst  Schulz1  derived 
the  following  empirical  formula: 

ff  X  «p  X  N  X  M} 


a  —  05OI2     X 


c, 

M  A 


=  =.  x  io-  x  ^-^^       '^,    (82) 

3  *->  A 

in  which  0a  =  rise  of  armature  temperature,  in  degrees  Centi- 
grade; 

6  =  factor  of  magnetic  saturation  in  smallest  cross- 
section  of  armature  core, 

-4-  18,000  =  (Ba  -+-  18,000. 


2  np  X  b&  X  /a  X  £, 

(?>  =  useful  flux  through  armature,  in  webers; 
2  #p  =  number  of  poles; 

^a   X   /a   X   <&2  =  net  area  of  least  cross-sec- 
tion of  armature  core,  in  square  centi- 
metres; 
(Ba  =  flux-density     in     armature      core,      in 

gausses; 

N  =  number  of  revolutions  per  minute; 
M\  —  mass  of  armature  core,  in  cubic  centimetres; 
6"A  =  surface  of  armature-core,  in  square  centimetres, 

,     <4*    7T     , 

=  c/a  TT  X  4  H~ »  i°r  smooth  armatures, 

=  d"&  n  X  /a  +  •       — ,   for    toothed  and  perforated 
armatures. 

The  numerical  constant  in  this  formula  is  averaged  from 
values  ranging  between  .008  and  .012  for  smooth-core  machines, 
and  between  .010  and  .0125  for  toothed  armatures. 


1  Ernst    Schulz,    Elektrotechn.  Zeitschr.,    vol.    xiv.    p.    367  (June  30,  1893); 
Electrical  World,  vol.  xxii.  p.  118  (August  12,  1893). 


13°  DYNAMO-ELECTRIC  MACHINES.  [§37 

Translating  (82)  into  the  English  system  of  measurement, 
we  obtain  the  formula: 


00045 


0a  =  rise  of  armature  temperature,  in  degrees  Centigrade; 
(B"a  =  density  of  magnetization,  in  lines  per  square  inch; 
np  =  number  of  pairs  of  poles; 
JV  =  number  of  revolutions  per  minute; 
M  =  mass  of  iron,  in  cubic  feet; 
6"A  =  armature  core  surface,  in  square  inches. 

The  value  of  the  constant  in  the  English  system,  for  the 
type  of  machines  experimented  upon  by  Schulz,  varies  between 
the  limits  .0003  and  .0005. 

The  numerical  factor  depends  upon  the  units  chosen,  upon 
the  ventilation  of  the  armature,  upon  the  quality  of  the  iron, 
and  upon  the  thickness  of  the  lamination,  and  consequently 
varies  considerably  in  different  machines.  For  this  reason  it 
is  advisable  not  to  use  formula  (82)  or  (83),  respectively,  except 
in  case  of  calculating  an  armature  of  an  existing  type  for  which 
this  constant  is  known  by  experiment.  In  the  latter  case, 
Schulz's  formula,  although  not  as  exact,  is  even  more  con- 
venient than  the  direct  equation  (81)  which  necessitates  the 
separate  calculation  of  the  energy  losses,  while  (82)  and  (83) 
contain  the  factors  determining  these  losses,  and  therefore 
will  give  the  result  quicker,  provided  that  the  numerical  factor 
has  been  previously  determined  from  similar  machines. 

Another  empirical  formula  for  the  temperature  increase  of 
drum  armatures,  which,  however,  requires  the  specific  energy- 
loss  to  be  calculated,  and  which  therefore  is  not  as  practical  as 
that  of  Schulz,  and  which  cannot  give  as  accurate  results  as 
can  be  obtained  by  the  use  of  Table  XXXVI.  in  connection 
with  formula  (81),  has  recently  been  given  by  Ernest  Wilson.1 

37.  Circumferential  Current  Density  of  Armature. 

An  excellent  check  on  the  heat  calculation  of  the  armature, 
and  in  most  cases  all  that  is  really  necessary  for  an  examina-' 


1  Ernest  Wilson,  Electrician  (London),  vol.  xxxv.  p.  784  (October  n,  1895); 
Elektrotechn.  Zeitschr.,  vol.  xvi.  p.  712  (November  7,  1895). 


§37]  ENERGY  LOSSES  IN  ARMATURE.  131 

tion  of  its  electrical  qualities,  is  the  computation  of  the  cir- 
cumferential current  density  of  the  armature.  This  is  the 
sum  of  the  currents  flowing  through  a  number  of  active  arma- 
ture conductors  corresponding  to  unit  length  of  core-periphery, 
and  is  found  by  dividing  the  total  number  of  amperes  all 
around  the  armature  by  the  core  circumference: 

I' 

•;"  -  -      ^=i¥?; ^ 

ic  =  circumferential  current  density,  in  amperes  per  inch 
length  of  core  periphery,  or  in  amperes  per  centi- 
metre; 
Nc  =  total   number   of    armature   conductors,   all  around 

periphery; 

/'  =  total  current  generated  in  armature,  in  amperes; 
2  n'p  =  number   of    electrically  parallel   armature  portions, 
eventually  equal  to  the  number  of  poles; 

=  current  flowing  through  each  conductor,  in  amperes; 


2  n 


f 

Nc  X  —  r  —  total  number  of  amperes  all  around  armature; 
2  np 

this  quantity  is  called  "volume  of  the  armature  cur- 
rent" by  W.  B.  Esson,  and  "circumflux  of  the  arma- 
ture" by  Silvanus  P.  Thompson; 

<4  =  diameter  of  armature  core,  in  inches;  in  case  of  a 
toothed  armature,  on  account  of  the  considerably 
greater  winding  depth,  the  external  diameter,  d"M 
is  to  be  taken  instead  of  dM  in  order  to  bring 
toothed  and  smooth  armatures  to  about  the  same 
basis;  for  a  similar  reason,  for  an  inner-pole  dy- 
namo, the  mean  diameter,  d'"M  should  be  substituted 
for  d&. 

By  comparing  the  values  of  /c  found  from  (84)  with  the 
averages  given  in  the  following  Table  XXXVII.,  the  rise  of  the 
armature  temperature  can  be  approximately  determined,  and 
thus  a  measure  for  the  electrical  quality  of  the  armature  be 
gained.  The  degree  of  fitness  of  the  proportion  between  the 
armature  winding  and  the  dimensions  of  the  core  is  indicated  by 


I32 


D  YNAMO-ELECTRIC  MA  CHINES, 


[§38 


the  amount  of  increase  of  the  armature  temperature.  If  the 
latter  is  too  high,  it  can  be  concluded  that  the  winding  is  pro- 
portioned excessively,  and  either  should  be  reduced  or  divided 
over  a  larger  armature  surface : 

TABLE  XXXVII. — RISE  OF  ARMATURE  TEMPERATURE,  CORRESPONDING 
TO  VARIOUS  CIRCUMFERENTIAL  CURRENT  DENSITIES. 


CIRCUMFERENTIAL 

RISE  OP  ARMATURE  TEMPERATURE,  0a. 

High  Speed  (Belt-Driven) 
Dynamos. 

Low  Speed  (Direct-Driven) 
Dynamos. 

per  inch. 

per  cm. 

Centigrade. 

Fahrenheit. 

.  Centigrade. 

Fahrenheit. 

50  to  100 

20  to    40 

15°  to   25° 

27°  to  45° 

10°  to  20° 

18°  to  36° 

100 

200 

40 

80 

20 

35 

36 

63 

15 

25 

27 

45 

200 

300 

80 

120 

30 

50 

54 

90 

20 

35 

36 

63 

300 

400 

120 

160 

40 

60 

72 

108 

25 

40 

45 

72 

400 

500 

160 

200 

50 

70 

90 

126 

30 

45 

54 

81 

500 

600 

200 

240 

60 

80 

108 

144 

35 

50 

63 

90 

600 

700 

240 

280 

70 

90 

126 

162 

40 

60 

72 

108 

700 

800 

280 

320 

80 

100 

144 

180 

50 

70 

90 

126 

The  difference  in  the  temperature-rise  at  same  circumferen- 
tial current  density  for  high-speed  and  low-speed  dynamos 
(columns  3  and  5,  or  4  and  6,  respectively,  of  the  above  table) 
is  due  to  the  fact  that,  other  conditions  being  equal,  in  a  low- 
speed  machine  less  energy  is  absorbed  by  hysteresis  and  eddy 
currents;  that,  consequently,  less  total  heat  is  generated  in 
the  armature,  and,  therefore,  more  cooling  surface  is  available 
for  the  radiation  of  every  degree  of  heat  generated. 

38.  Load  Limit  and  Maximum  Safe  Capacity  of  Arma- 
tures. 

From  Table  XXXVII.  also  follows  that,  according  to  the 
temperature  increase  desired,  the  load  carried  by  an  arma- 
ture varies  between  50  and  800  amperes  per  inch  (=  20  to  320 
amperes  per  centimetre)  of  circumference,  or  between  about 
150  and  2,500  amperes  per  inch  (=  60  to  1,000  amperes  per 
centimetre)  of  armature  diameter.  As  a  limiting  value  for 
safe  working,  Esson1  gives  1,000  amperes  per  inch  diameter 
(—  600  amperes  per  centimetre)  for  ring  armatures,  and  1,500 

1  Esson,  Journal  I.  E.  £.,  vol.  xx.  p.  142.     (1890.) 


§38]  ENERGY  LOSSES  IN  ARMATURE.  133 

amperes  (=  400  amperes  per  centimetre)  for  drums.  Kapp1 
allows  2,000  amperes  per  inch  (=  800  amperes  per  centimetre) 
diametral  current  density  for  diameters  over  12  inches  as  a 
safe  load. 

Taking  1,900  amperes  per  inch  diameter  (=  600  amperes  per 
inch  circumference)  as  the  average  limiting  value  of  the  arma- 
ture-load in  high-speed  dynamos,  corresponding  to  a  tempera- 
ture rise  of  about  70°  to  80°  Centigrade  (=  126°  to  144° 
Fahrenheit),  compare  Table  XXXVII.  ,  we  have: 

N°  X  =  W0  x  <*» 


and  since  for  the  total  electrical  energy  of  the  armature  we 
can  write,  see  formula  (136),  §56, 

AT     y    <f)  v     A/~ 
D'    _     J?>    v     /'    _     -LVc    A     ^  A    ^v  ,-,  /ftA\ 

-  ^X   io8  X  60  X  I  '      ~™ 

in  which  P'  —  total  electrical    energy  generated   in  dynamo, 

in  watts; 

El  —  total  E.  M.  F.,  generated  in  armature,  in  volts; 
/'  —  total   current   generated    in   armature,  in  am- 

peres; 

JVC  =  number  of  armature  conductors; 
$  =  number  of  useful  lines  of  force; 
N  =  speed,  in  revolutions  per  minute; 
#'p  =  half    number    of    parallel     armature    circuits 

(eventually  also  number  of  pairs  of  poles); 

we  obtain  for  the  limit  of  the  capacity,  by  inserting  (85)  into 
(86): 

*JL^=  63  x  to-  x  <4x  N  x  9.    (87) 


But   the  useful  flux,  $,  is,  the  product  of  gap  area  and  field 
density,  or,  approximately, 


Kapp,  S.  P.  Thompson's  "Dynamo-Electric  Machinery,"  4th  edition,  p.  439. 


134  DYNAMO-ELECTRIC  MACHINES.  [§38 

and  consequently  the  safe  capacity  of  a  high-speed  dynamo  : 

p'  =  63  x  10  -8  x  d&  x  N  x  d^^-  x  ft\  x  4  x  oe" 
=  lo-6  x  <4'  x  4  x  /?',  x  ^  x  oe"  .........  (88) 

For  low-speed  machines,  2,500  amperes  per  inch  diameter,  or 
800  amperes  per  inch  circumference,  can  safely  be  allowed, 
hence,  in  order  to  obtain  the  safe  capacity  of  a  direct-driven  machine, 
the  factor  i.jj  must  be  adjoined  to  formula  (88). 


In  (88),  P'  =  maximum  safe  capacity  of  armature,  in  watts; 
d&  =:  diameter  of  armature  core,  in  inches; 
/a  =  length  of  armature  core,  in  inches; 
fi1  'x  =  percentage  of  useful  gap  circumference;  to  be 
taken  somewhat  higher  than  the  percentage 
of   polar  arc,    to  allow   for  circumferential 
spread    of    the   lines   of    force,    see   Table 
XXXVIII.  ; 

3C"  =  field  density,  in  lines  of  force  per  square  inch; 
N  =  speed,  in  revolutions  per  minute. 

Inserting  into  (85)  the  equivalent  limit  current  density  in 
metric  units,  of  240  amperes  per  centimetre  circumference 
(=  765  amperes  per  centimetre  diameter),  the  maximum  safe 
capacity,  in  watts,  of  a  high-speed  armature  given  in  metric 
measure  is  obtained  : 

P'  =  765    X  d&  x  W  X  $ 
io8  X  3° 

=  4  X  io-7  X  d;  X  /a  X  ft\  X  N  X  OC,      .  .(89) 

wherein  all  dimensions  are  expressed  in  centimetres.  For 
low-speed  machines  the  factor  4  in  this  formula  must  be  replaced 
by  5-33-  Average  values  for  /3\,  taken  from  practice,  are 
given  in  Table  XXXVIII.  on  the  opposite  page. 

In  this  table  the  percentages  given  for  toothed  arma- 
tures refer  to  straight  tooth  cores  only;  for  projecting  teeth 
a  value  between  the  straight  tooth  and  the  perforated  arma- 
ture should  be  taken,  proportional  to  the  size  of  the  opening 
between  the  tooth  projections. 


§39] 


ENERGY  LOSSES  IN  ARMATURE. 


TABLE  XXXVIII. — PERCENTAGE  OP   EFFECTIVE    GAP   CIRCUMFERENCE 
FOR  VARIOUS  RATIOS  OF  POLAR  ARC. 


PERCENTAGE  OF  EFFECTIVE  GAP  CIRCUMFERENCE. 

PERCENTAGE 

OF 

2  Poles. 

4  to  6  Poles. 

8  to  12  Poles. 

14  to  20  Poles. 

POLAR  ARC. 

fc 

*g  *  1         • 

fc    • 

* 

/? 

o  ^  o 

^2 

O  ^  c5 

•02 

O  <£,  4> 

r^    Q> 

A 

^"S  _s 

,s"H  5       -c-2       .elS-H  '    -a  2 

agS 

,-  = 

pi 

if 

|s 

w 

is    §£s 

£-1  *jj            p  OJ  t; 

§1 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

.95 

.98 

.96 

.97 

.955 

.965 

.955 

.96 

.955 

.90 

.96 

.915 

.94 

.91 

.93 

.91 

.92 

.91 

.85 

.94 

.87 

.905 

.865 

.89 

.865 

.88 

.865 

.80 

.91 

.825 

.87 

'.82 

.85 

.82 

.84 

.82 

.75 

.88 

.78 

.835 

.775 

.815 

.775 

.80 

.775 

.70 

.85 

.735 

.80 

.73 

.78 

.725 

.76 

.725 

.65 

.82 

.69 

.765 

.685 

.74 

.68 

.72 

.675 

.60 

.78 

.645 

.73 

.635 

.70 

.63 

.68 

.625 

.55 

.74 

.60 

.69 

.59 

.665 

.58 

.64 

.575 

.50 

.70 

.55 

.65 

.54 

.625 

.53 

.60 

.525 

39.  Running  Yalue  of  Armature. 

In  order  to  form  an  idea  of  the  efficiency  of  an  armature  as 
an  inductor,  its  "running  value"  has  to  be  determined. 

In  forming  the  quotient  of  the  total  energy  induced  by  the 
product  of  the  weight  of  copper  on  the  armature  and  the  field 
density,  the  number  of  watts  generated  per  pound  of  copper  at 
unit  field  density  is  obtained,  an  expression  which  indicates 
the  relative  inducing  power  of  the  armature: 


£'  x  r 

>4  x  JC" 


(90) 


P'&  —  running  value  of  armature  in  watts  per  unit  weight 
of  copper,  at  unit  field  density; 

E[  —  total  E.  M.  F.  generated  in  armature,  in  volts; 
/'  =  total  current  generated  in  armature,  in  amperes; 

wt&  —  weight  of  copper  in  armature,  in  pounds  or  in  kilo- 
grammes, formula  (58); 

JC"  =  field  density,  in   lines  of  force  per  square  inch,  or 
per  square  centimetre,  respectively. 


136 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§39 


The  value  of  P'&  for  a  newly  designed  armature  being  found, 
its  relative  inductor  efficiency  can  then  be  judged  at  by  com- 
parison with  other  machines.  The  running  value  of  modern 
dynamos,  according  to  the  type  of  machine  and  the  kind  of 
armature,  varies  between  very  wide  limits,  and  the  following 
are  the  averages  for  well-designed  machines: 

TABLE  XXXIX.— RUNNING  VALUES  OF  VARIOUS  KINDS  OF  ARMATURES. 


TYPE  OF  MACHINE. 

KIND 

OF 

ARMATURE. 

RUNNING  VALUE,  P'a 
(Watts  per  unit  weight  of  copper 
at  unit  field  density.) 

English  Measure. 

Metric  Measure. 

Watts  per  Ib.  at 
1  line  per  sq.  inch. 

Watts  per  kg.  at 
1  line  per  cm.2 

High 
Speed 

Bipolar 

Drum 

.015      to  .03 

.045  to  .09 

Ring 

.01        "  .02 

.03    "  .06 

Multipolar 

Drum 

.01        "  .02 

.03    "  .06 

Ring 

.0075    "  .015     |       .022"  .045 

Low 
Speed 

Bipolar 

Drum   I 

.0075     "  .015 

.022"  .045 

Ring    ! 

.005      "  .01 

.015"  .03 

Multipolar 

Drum 

.005      "  .01 

.015"  .03 

Ring 

.00375  "  .0075 

.011"  .022 

CHAPTER  VII. 

MECHANICAL    EFFECTS   OF    ARMATURE   WINDING. 

4:0.  Armature  Torque, 

The  work  done  by  the  armature  of  a  dynamo  can  be  ex- 
pressed in  two  ways:  electrically,  as  the  product  of  E.  M.  F. 
and  current  strength, 

P1  =  £'  X  /'  watts; 

and  mechanically,  as  the  product  of  circumferential  speed  and 
turning  moment,  or  torque, 

P'  =  27txNxrx      74    -  -  =  .  142  x  N  X  r  watts; 
33,000 

P'  =  total  energy  developed  by  machine,  in  watts; 
E'  =  total  E.  M.  F.  generated  in  armature,  in  volts; 
/'  ==  total  current  generated  in  armature,  in  amperes; 
N  —  speed,  in  revolutions  per  minute; 
t  —  torque,  in  foot-pounds; 

746  —  number  of  watts  making  one  horse  power; 
33,000  =  number   of    foot-pounds    per    minute    making   one 

horse  power. 
Equating  the  above  two  expressions,  we  obtain: 

£'  X  I'  =  .142  X  N  x  r, 
from  which  follows  : 

£'  X  /'  E'  X  I1 

r  =  .142  X  N  =  7'°42  X  ~^~W~~  foot-P°unds-   -.(91) 

Or,  in  metric  system,  i  kilogramme-metre  being  =  7.233  foot- 
pounds, 

'  (92) 


Inserting  into  (91)  and  (92)  the  expression  for  the  E.  M.  F. 
from  §  56,  viz.: 

7\T      N/      (ft      V      A7^ 

T"l    f C        ^*  r\       •*•  W 

£L,      "==• 


n'X  io8  X  60' 


p 
137 


I38  DYNAMO-ELECTRIC  MACHINES.  [§41 

the  equation  for  the  torque  becomes: 

Ne  x  $  X  N         I' 

^•°42  x  .7x  10*  x  60  >    7y 

=  ~     if-  X  —  -  X  ^c  X  $  foot-pounds  ^ 
10  n  p 

J-  ......  (93) 

I    62?  /' 

=  -jj?  X  ^-  X  ^c  X  ^  kg.  -metres     J 

from  which  follows  that  in  a  given  machine  the  torque  depends 
in  nowise  upon  the  speed,  but  only  upon  the  current  flowing 
through  the  armature,  and  upon  the  magnetic  flux. 

41.  Peripheral  Force  of  Armature  Conductors. 

By  means  of  the  armature  torque  we  can  now  calculate  the 
drag  of  the  armature  conductors  in  a  generator,  respectively 
the  pull  exerted  by  the  armature  conductors  in  a  motor. 

The  torque  divided  by  the  mean  radius  of  the  armature 
winding  gives  the  total  peripheral  force  acting  on  the  arma- 
ture; and  the  latter,  divided  by  the  number  of  effective  con- 
ductors, gives  the  peripheral  force  acting  on  each  armature 
conductor.  In  English  measure,  if  the  torque  is  expressed  in 
foot-pounds  and  the  radius  of  the  winding  in  inches,  the 
peripheral  force  of  each  conductor  is: 


P°unds 


x  ^vc  x  p\ 

Inserting  into  this  equation  the  value  of  t  from  formula  (91), 
we  obtain : 

E'   x   I'  ft 

24  x  7-042  X      —ft- 


2  X  7-042   X  n  E'  x  /' 

/\ 


60  ...         ...... 

X  Nc  X  ft\, 


60  12 

\ 

or, 

;    -...(95) 


§41]  EFFECTS  OF  ARMATURE    WINDING.  139 

/a  =  peripheral  force  per  armature  conductor,  in  pounds; 
E'  x  /'  =  total  output  of  armature,  in  watts; 

vc  —  mean  conductor  velocfty,  in  feet  per  second; 
Nc  =  total  number  of  armature  conductors; 
fi\  =  percentage  of  effective  armature  conductors,  see 

Table  XXXVIII.  ,  §  38. 

A  second  expression  for  the  peripheral  force  can  be  obtained 
by  substituting  in  the  original  equation  (94)  the  value  of  r  from 
formula  (93),  thus: 

f  -  24x  11.74    _/;       ^c     x  * 

<  «;  x  NC  x  ft\  x  <*'* 

2.82  /'  X    # 


Replacing  in  this  the  useful  flux  $  by  its  equivalent,  the 
product  of  gap  area  and  field  density,  we  find  a  third  formula 
for  the  peripheral  force: 

2.82  r    X    *'•>   X     ~    X    ?>    X    *'    X    *' 

/a  —  ~Ts~ 


I0  «       X        a    X 


___     T"  ^"O     \/  v/     7      \/     *i/"> ^   v\/\ t * «^ rl e  •  / O ^ \ 

—    ^-    A     — r     A    *a    A    wt>     pUUIlUb ,        V.t''/ 

IO  n  p 

=  total  current  flowing  in  each  armature  conductor,  in 


amperes; 

4   =  length  of  armature  core,  in  inches; 
JC"    =  field  density,  in  lines  of  force  per  square  inch. 

If  the  dimensions  of  the  armature  are  given  in  centimetres, 
the  conductor  velocity  in  metres  per  second,  and  the  field 
density  in  gausses,  the  peripheral  force  is  obtained  in  kilo- 
grammes from  the  following  formulae: 

/a  =  '  I02  X  vc  x  j£  X  p\  kil°Srammes' 
/a  =  X  ' 


«'p  X          X   ft' 

and 

/a  =  ^4  X  -r  X  /a  X  5C  kilogrammes,      .  ..(100) 

n  P 
which  correspond  to  (95),  (96)  and  (97),  respectively. 


14°  DYNAMO-ELECTRIC  MACHINES.  [§42 

It  is  on  account  of  this  peripheral  force  exerted  by  the 
magnetic  field  upon  the  armature  conductors  that  there  is  need 
of  a  good  positive  method  *of  conveying  the  driving  power 
from  the  shaft  to  the  conductors,  or  vice  versa;  in  the  gener- 
ator it  is  the  conductors,  and  not  the  core  discs,  that  have  to 
be  driven;  in  the  motor  it  is  they  that  drive  the  shaft.  Thus 
the  construction  of  the  armature  is  aggravated  by  the  condi- 
tion that,  while  the  copper  conductors  must  be  mechanically 
connected  to  the  shaft  in  the  most  positive  way,  yet  they  must 
be  electrically  insulated  from  all  metallic  parts  of  the  core. 
In  drum  armatures  the  centrifugal  force  still  more  complicates 
matters  in  tending  to  lift  the  conductors  from  the  core;  in 
smooth  drum  armatures  it  has  therefore  been  found  necessary 
to  employ  driving  horns,  which  either  are  inserted  into  nicks 
in  the  periphery  of  the  discs,  or  are  supported  from  hubs 
keyed  to  the  armature  shaft  at  each  end  of  the  core.  In  ring 
armatures  the  centrifugal  force  presses  the  conductors  at  the 
inner  circumference  toward  the  armature  core,  and  thus  helps 
to  drive,  while  the  spider  arms,  by  interlocking  into  the  arma- 
ture winding,  serve  as  driving  horns.  If  toothed  discs  are 
used,  no  better  means  of  driving  can  be  desired. 

42.  Armature  Thrust. 

If  the  field  frame  of  a  dynamo  is  not  symmetrical,  which  is 
particularly  the  case  in  most  of  the  bipolar  types  (see  Figs.  77 
to  85),  unless  special  precautions  are  taken  there  will  be  a 
denser  magnetic  field  at  one  side  of  the  armature  than  at  the 
other,  and  an  attractive  force  will  be  exerted  upon  the  arma- 
ture, resulting  in  an  armature  thrust  toward  the  side  of  the 
denser  field. 

The  force  with  which  the  armature  would  be  attracted,  if 
only  one-half  of  the  field  were  acting,  is: 

/  =  2  it  X  ^L  X  (  — V  =  .0199  X  Sg  X  5C2  dynes, 

\47r/ 
or,  since  981,000  dynes  =  i  kilogramme, 

/  =  T  X  Sg  X  3C2  =  2.03  x  io~8  X  Sg  X  3C2  kilogrammes; 


Sg  =  gap  area,  in  square  centimetres; 

3C  =  field  density,  in  lines  of  force  per  square  centimetre. 


§42]  EFFECTS  OF  ARMATURE    WINDING.  I41 

Expressing  the  gap  area  by  the  dimensions  of  the  armature, 
we  obtain: 

/  =  2.03  X  io-8  x  ^~  x  4  x  ft\  x  oe2 

=  32  x  io-9  x  <4  X  4  X  /?',  X  OC2  kilogrammes.      .  .(101) 

If,  now,  both  halves  of  the  field  are  in  action,  but  one  half 
is  stronger  than  the  other,  the  armature  will  be  acted  upon  by 
two  forces: 

/!  =.32  X  io-9  X  <  X  4  X  ft\  X  OC;  kilogrammes, 

and 

/2  =  32  x  io-9  X  <4  X  4  X  /?'i  X  3C22  kilogrammes, 

and  will  be  drawn  toward  the  stronger  side  by  the  amount  of 
the  difference  of  their  attractive  forces.  The  armature  thrust, 
therefore,  is: 

/t=/1-/2^32xio-9x^x/ax^1x(ae12-ae22)kg.;    ...(102) 

/t  =  thrusting   force   acting   on  armature,    due   to   unsym- 

metrical  field,  in   kilogrammes; 
d&  =  diameter  of  armature,  in  centimetres; 
4  =  length  of  armature,  in  centimetres;  '/.. 

/3\  =  percentage  of   effect.  'ye  gap-circumference,  see  Table 

XXXVI.  ; 
5d  =  density   of  field,  on   stronger   side,   lines   per   square 

centimetre; 
3C2  =  density  of  field,  on  weaker  side,  lines  per  square  centi- 

metre. 

In  English  measure,  i  pound  being  =  .4536  kilogrammes, 
and  i  square  inch  =  6.4515  square  centimetres,  the  formula  for 
the  armature  thrust  becomes: 


X  4  X  ^',  X 


=  ii  Xio-9X^aX4X/^X(rcY-3e''22)  pounds,      ....(103) 

in  which  d&  and  /a  are  to  be  expressed  in  inches,  and  3C",  and 
3e"2  in  lines  per  square  inch. 

In  such  types,  where  the  attractive  force  of  the  field  mani- 
fests itself  as  a  downward  thrust,  as  in  those  shown  in  Figs. 


142 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§42 


78,  80,  82  and  85,  the  value  obtained  by  (102)  or  (103),  re- 
spectively, is  to  be  added  to  the  dead  weight  of  the  armature, 
in  order  to  obtain  the  total  down  thrust  upon  the  bearings. 
If,  however,  /t  is  an  -upward  thrust,  as  is  indicated  in  Figs.  77, 


Fig.  77- 


Fig.  78. 


Fig.  79- 


Fig.  80. 


Fig  81. 


Fig.  82. 


Fig.  83.  Fig.  84.  Fig.  85. 

Figs.  77  to  85. — Unsymmetrical  Bipolar  Fields. 

81  and  84,  the  down  thrust  upon  the  bearings  is  the  weight  of 
the  armature,  diminished  by  the  amount  of  ft.  In  the  cases 
illustrated  by  Figs.  79  and  83  the  action  of  the  field  causes  a 
sideward  thrust,  which  has  to  be  taken  care  of  by  a  proper 
design  of  the  bearing  pedestals,  or  of  the  journal  brackets. 


CHAPTER   VIII. 

ARMATURE    WINDING    OF    DYNAMO-ELECTRIC    MACHINES. 

4:3.  Types  of  Armature  Winding. 

a.   Closed  Coil  Winding  and  Open  Coil  Winding. 

If,  in  a  continuous  current  dynamo,  the  reversal  of  the  cur- 
rent would  take  place  in  all  the  conductors  at  once,  consider- 
able fluctuation  of  the  E.  M.  F.  would  be  the  result.  In  order 
to  obtain  a  steady  current,  the  armature  conductors  are,  there- 
fore, to  be  so  arranged  relative  to  the  poles,  that  a  portion  of 
them  is  in  the  strongest  part  of  the  field,  while  others  are 
exposed  to  a  weaker  field,  and  some  even  are  in  the  neutral 
position. 

After  having  thus  arranged  the  conductors,  their  connecting 
can  be  effected  by  one  of  the  following  two  methods : 

(I.)  All  conductors  are  connected  among  each  other  so  as  to 
form  an  endless  winding,  closed  in  itself,  and  consisting  of  two 
or  more  parallel  branches,  in  each  of  which  all  the  single 
E.  M.  Fs.  induced  have  the  same  direction,  and  in  which  the 
reversal  of  the  current  occurs  in  such  conductors  only  that  at 
the  time  are  in  the  neutral  position.  An  armature  with  such 
connections  is  called  a  closed  coil  armature  (Fig.  86). 

(II.)  The  conductors  are  joined  into  groups,  each  group  con- 
taining all  such  conductors  in  series  which,  relative  to  the 
field,  have  exactly  the  sam«  position;  and  the  current  is  taken 
off  from  such  groups  only  which  at  the  time  have  the  maximum, 
or  nearly  the  maximum,  E.  M.  F.,  all  other  groups  being  at 
that  time  cut  out  altogether.  An  armature  wound  in  this 
manner  is  styled  an  open  coil  armature  (Fig.  87). 

Although  in  a  closed  coil  armature  the  sum  of  all  the  E.  M. 
Fs.  of  the  single  coils  is  collected  by  the  brushes  (see  §  9), 
while  in  an  open  coil  armature  the  E.  M.  F.  of  one  group  of 
coils  only  is  delivered  to  the  external  circuit,  and  although, 
therefore,  the  total  E.  M.  F.  output  of  an  armature  is  smaller 
when  connected  up  in  the  open  coil  fashion  than  it  would  be  if 


144  DYNAMO-ELECTRIC  MACHINES.  [§43 

the  same  armature  were  run  at  the  same  speed  but  connected 
by  the  closed  coil  method,  yet  an  open  coil  armature  offers 
great  advantages  in  case  of  high  potential  machines,  as  there 
is  no  difference  of  potential  between  adjoining  commutator 
bars  belonging  to  different  groups  of  coils  and  only  a  small 


Fig.  86. — Closed  Coil  Winding.  Fig.  87. — Open  Coil  Winding. 

number  of  segments  is  required  to  bring  the  fluctuation  of  the 
E.  M.  F.  within  practical  limits.  Open  coil  armatures  are 
therefore  preferable  to  closed  coil  ones  in  case  of  machines 
for  series  arc  lighting,  where,  if  closed  coil  windings  are  em- 
ployed, a  great  number  of  commutator  segments  is  required 
on  account  of  the  high  total  potential  around  the  commutator. 
(See  Table  XXL,  §  25.) 

b.    Spiral  Winding,  Lap  Winding,  and  Wave  Winding. 

According  to  the  manner  in  which  the  connecting  of  the 
conductors  by  the  above  two  methods  is  performed,  the  fol- 
lowing types  of  armature  windings  can  be  distinguished: 

(1)  Spiral  Winding,  or  Ring  Winding,  Figs.  88  and  89; 

(2)  Lap  Winding,  or  Loop  Winding,  Figs.  90  and  91; 

(3)  Wave  Winding  or  Zigzag  Winding,  Figs.  92  and  93. 

In  the  spiral  winding,  Figs.  88  and  89,  which  can  be  applied 
in  the  case  of  ring  armatures  only,  the  connecting  conductors 
are  carried  through  the  interior  of  the  ring  core,  and  the  wind- 
ing thus  constitutes  either  one  continuous  spiral,  Fig.  88,  from 
which,  at  equal  intervals,  branch  connections  are  led  to  the 
commutator,  or  a  set  of  independent  spirals,  Fig.  89,  which 
are  separately  connected  to  the  commutator. 


§43] 


ARMATURE    WINDING. 


145 


The  lap  winding,  as  well  as  the  wave  winding,  is  executed  en- 
tirely exterior  to  the  core,  and  can  be  applied  to  both  drum 
and  ring  armatures. 

In  the  lap  winding,   Figs.   90  and  91,   the  end  of  each  "Coil, 


Figs.  88  and  89.— Spiral  Windings. 

consisting  of  two  or  more  conductors  situated  in  fields  of 
opposite  polarity,  is  connected  through  a  commutator  segment 
to  the  beginning  of  a  coil  lying  within  the  arc  embraced  by 
the  former.  With  reference  to  the  direction  of  connecting, 


Fig.  90. — Lap  Winding. 

therefore,  the  beginning  of  every  following  coil  lies  back  of 
the  end  of  the  foregoing,  and  the  winding,  consequently, 
forms  a  series  of  loops,  which  overlap  each  other.  Fig.  90 
represents  such  a  lap  winding  for  a  four-pole  drum  armature, 
the  development  of  which,  Fig.  91,  more  clearly  shows  the 
forming  of  the  loops  and  the  manner  of  their  overlapping. 


146 


DYNAMO-ELECTRIC  MACHINES. 


[§43 


In  the  wave  winding,  Figs.  92  and  93,  the  connecting  contin- 
ually advances  in  one  direction,  the  end  of  each  coil  being 
connected  to  the  beginning  of  the  one  having  a  corresponding 
position  under  the  next  magnet  pole;  and  the  winding,  in  con- 


^    </ 


_ 


ie 


O^Qcf^j^Q  CJ  ^U^D    HH 

-t-  4- 

Fig.  91. — Development  of  Lap  Winding. 

sequence,  represents  itself  in  a  zigzag,  or  wave  shape.  The 
wave  winding  is  illustrated  in  Fig.  92,  and  for  better  compari- 
son the  same  four-pole  drum  armature  is  chosen  that  in  Fig. 


Fig.  92. — Wave  Winding. 

90  is  shown  with  a  lap  winding.  The  development  given  in 
Fig.  93  distinctly  shows  the  zigzag  form  of  the  wave  winding. 
In  multipolar  machines,  the  wave  winding  can  be  used  for 
series  as  well  as  for  parallel  connection;  the  lap  winding, 
however,  for  parallel  grouping  only. 


§44] 


ARMATURE    WINDING. 


While  the  lap  winding  necessitates  as  many  sets  of  brushes 
as  there  are  magnet  poles,  the  wave  winding  for  any  number 
of  poles  invariably  needs  but  two  sets  of  brushes. 


/OOO< 

d|   I     e|   I     f|  |      g[  |      h| 
Fig.  93. — Development  of  Wave  Winding. 

For  series-parallel  connection,  either  wave  winding,  may  be 
used  or  lap  and  wave  windings  may  be  combined.  Fig.  94 
represents  the  development  of  such  a  * '  mixed  winding, "  the 


Fig.  94. — Development  of  "  Mixed  "  Winding. 

coils  partly  being  connected  in  the  lap  and  partly  in  the  wave 
fashion.  This  winding,  like  the  wave  winding,  has  the  pecul- 
iarity of  requiring  but  two  sets  of  brushes,  independently  of 
the  number  of  magnet  poles. 

44.  Grouping  of  Armature  Coils. 

When  the  conductors  of  a  continuous  current  armature,  as  is 
usually  the  case,  are  to  be   so   connected   among  each   other 


148  DYNAMO-ELECTRIC  MACHINES.  [§44 

that  the  completed  arrangement  forms  one  continuous  winding, 
or  several  separate  continuous  windings  re-entrant  on  them- 
selves, that  is,  when  the  armature  is  to  have  a  closed  coil 
winding,  then,  according  to  the  voltage  desired,  the  different 
conductors,  or  coils,  may  be  grouped  in  two  or  more  parallel 
circuits.  In  bipolar  machines  having  the  armature  coils  ar- 
ranged in  a  single  re-entrant  winding,  there  can  be  but  two 
such  paths,  the  current  bifurcating  only  once,  dividing  at  the 
negative  brush  and  reuniting  at  the  positive  brush  as  it  leaves 
the  armature.  In  multipolar  dynamos,  however,  there  may 
be  more  than  one  bifurcation  in  each  re-entrant  winding,  and 
the  current,  therefore,  split  up  into  more  than  two  electrically 
parallel  paths.  When  there  is  but  one  bifurcation  of  the  cur- 
rent, independent  of  the  number  of  poles,  the  armature  is  said 
to  have  a  series  grouping,  or  a  two-circuit  winding;  but  when 
there  are  as  many  parallel  branches  in  each  winding  as  there 
are  poles  in  the  field-frame,  the  armature  coils  are  said  to  be 
arranged  in  parallel  grouping,  or  in  multiple  circuit  winding; 
finally,  when  the  number  of  the  bifurcations  of  the  current  in 
each  winding  is  greater  than  one  and  less  than  the  number  of 
poles,  we  have  a  combination  of  the  above  two  methods,  and 
the  coils  are  arranged  in  what  is  called  series-parallel  or  mixed 
grouping. 

An  armature  with  series  grouping  requires  but  two  sets 
of  brushes  at  neutral  points  of  the  commutator,  while  one 
with  parallel  grouping  of  the  coils  needs  as  many  sets  of 
brushes  as  there  are  poles.  The  number  of  brushes  required 
with  a  mixed  winding  is  greater  than  two  and  less  than  the 
number  of  poles,  and  is  given  by  the  number  of  parallel 
branches  in  each  of  the  re-entrant  windings. 

While  closed  coil  armatures  usually  form  but  one  single  re- 
entrant winding,  in  armatures  for  very  large  current  output  in 
which  a  difficulty  in  commutation  is  likely  to  arise  if  but  one 
winding  is  employed,  it  is  of  advantage  to  have  two  or  more 
distinct  re-entrant  windings,  each  connected  to  its  own  set  of 
commutator  bars,  all  the  sets  being  interleaved  in  one  commu- 
tator. The  current  from  such  armatures  is  collected  by  very 
thick  brushes  covering  two  or  more  consecutive  commutator 
bars,  or  by  sets  of  several  thin  brushes,  connected  in  parallel 
with  each  other  so  as  to  virtually  form  thick  brushes.  If  only 


§44]  ARMATURE    WINDING.  149 

one  commutator  bar  under  each  brush  actually  commu- 
tates  the  entire  armature  current,  as  shown  in  Fig.  95,  the 
winding  is  called  a  simplex,  or  a  single,  or  an  ordinary  winding; 
if,  however,  the  coils  are  so  grouped  in  a  number  of  independ- 
ent single  windings  that  the  current  is  commutated  at  several 
different  parts  of  the  contact  surface  of  the  brush,  each  inde- 
pendent volume  of  the  current  being  a  corresponding  fraction 
of  what  it  would  be  for  a  simplex  winding,  then  we  have  a  mul- 


Fig.  95. — Diagram  of  Simplex  Fig.  96. — Diagram  of  Duplex 

Winding.  Winding. 


tiplex  or  a  multiple  winding.  Fig.  96  gives  the  diagram  of  a 
duplex  or  double  winding,  having  two  commutating  segments 
under  each  brush.  If  there  are  three  points  of  commutation 
under  each  brush,  corresponding  to  three  independent  re-en- 
trant windings,  we  have  a  triplex  or  a  triple  winding,  and  so 
forth. 

In  a  multiplex  winding  the  successive  commutator  bars  of 
one  winding  are  not  adjacent  to  each  other,  but  alternate  with 
the  bars  of  the  other  windings,  the  result  being  that  a  section 
is  very  unlikely  to  be  short-circuited  by  dirt  or  by  an  arc. 
The  winding  is  very  flexible  owing  to  the  readiness  with  which 
any  number  of  independent  parallel  circuits  can  be  arranged. 
The  division  of  what  would  otherwise  be  a  very  heavy  con- 
ductor into  several  smaller  conductors,  also  has  the  effect  of 
reducing  the  eddy  current  loss  in  the  armature  winding. 

Considering  a  simplex  winding,  according  to  the  grouping 
of  the  conductors  or  coils,  the  endless  winding,  when  starting 
from  any  point  within  itself,  has  to  be  followed  either  once  or 
more  times  around  the  armature  in  order  to  return  to  the 


150  DYNAMO-ELECTRIC  MACHINES.  [§44 

starting  point.  If  the  whole  winding,  following  coil  by  coil  in 
the  order  as  actually  connected,  can  be  gone  over  in  but  one 
passage  around  the  armature,  Fig.  97,  the  winding  is  said  to 
be  singly  re-entrant,  if  the  armature  has  to  be  encircled  twice  to 


Fig.  97. — Singly  Re-entrant 
Winding. 


Fig.  98. — Doubly  Re-entrant 
Winding. 


return  to  the  starting  point,  as  in  Fig.   98,  we  have  a  doubly 
re-entrant  winding,  and  so  on. 

Using  a  circle  O  as  the  symbol  for  a  single  re-entrancy,  a 
single  loop  (2)  for  a  double  re-entrancy,  a  double  loop  (SS)  for 
a  triple  re-entrancy,  and  so  forth,  we  can  indicate  the  different 
kinds  of  windings  as  follows: 

TABLE  XL. — SYMBOLS  FOR  DIFFERENT  KINDS.  OF  ARMATXJRE  WINDINGS. 


KIND  OF  WINDING 


SINGLY 
REENTRANT 


DOUBLY 
REENTRANT 


TRIPLY 
REENTRANT 


QUADRUPLY 
REENTRANT 


SIMPLEX  WINDING 


0 


DUPLEX  WINDING 


oo 


©(2) 


TRIPLEX  WINDING 


OOO 


(5)©® 


QUADRUPLEX  WINDING 


oooo 


(2)©®© 


According  to  the  manner  of  grouping  and  to  the  kind  of 
winding  chosen,  the  voltage  generated  in  the  armature  by  a 
certain  number  of  conductors  (100),  at  a  certain  flux  (i  mega- 
line  =  1,000,000  lines  of  force,  per  pole)  and  at  a  certain  cut- 
ting speed  (100  revolutions  per  minute),  varies  between  the 
following  limits: 


§44] 


ARM  A  TURE    WINDING. 


TABLE  XLI. — E.  M.  F.  GENERATED  IN  ARMATURE,  AT  VARIOUS 
GROUPING  OF  CONDUCTORS. 


VOLTS  GENERATED 

AVERAGE  VOLTS 

PER   100   CONDUCTORS, 

BETWEEN  COMMUTATOR  SEGMENTS 

PER  100  REVOLUTIONS  PER  MIN. 

PEU  MEGALINE  AND  PER  100  REVS.  P.  M. 

AND  1  MEGALINE  FLUX  PER  POLE. 

(Independent  of  Number  of 

<. 

Conductors). 

i 

SERIES 
GROUPING. 

PARALLEL 
GROUPING. 

SERIES 
GROUPING. 

PARALLEL 
GROUPING. 

<2 

3 

H  ib 

Ms 

gg, 

«  be 

ss 

M  fci) 

gg 

if 

gf 

$$ 

I! 

H  be 

S* 

« 

"ot-5 

"SrS 

§3 

"a'-S 

"B.'S 

•T& 

"5<3 

g-f 

"5^5 

"D.-C 

1 

I'l 

s  o 

gl 

£  a 

fig 

'^ 

8  c 

=  .2 

H 

gjB 

Sl 

E| 

2 

1.667 

.833 

.556 

1.667 

.833 

.556 

.067 

.033 

.022 

.067 

.0331  .022 

4 

3.333 

1.66711.111 

1.667 

.833 

.556 

.267 

.1331  .089 

.133 

.067 

.044 

6 

5.000 

2.500 

1.667 

1.667 

.833 

.556 

.600 

.300 

.200 

.200 

.100 

.067 

8 

6.667 

3.333 

2.222 

1.667 

.833 

.556 

1.067 

.533 

.356 

.267 

.133 

.089 

10 

8.333 

4.167 

2.778 

1.667 

.833 

.556 

1.667 

.833 

.556 

.333 

.167 

.111 

12 

10.000 

5.000 

3.333 

1.667 

.833 

.556 

2.400 

1.200 

.800 

.400 

.200 

.133 

14 

11.667 

5.833 

3.889 

1.667 

.833 

.556 

3.267 

1.633 

1.089 

.467 

.233 

.156 

16 

13.333 

6.667 

4.444 

1.667 

.833 

.556 

4.267 

2.133 

1.422 

.533 

.267 

.178 

Designating  the  voltages  in  columns  2  to  7  of  this  table  by 
<?0,'the  number  of  conductors  required  for  any  particular  case 
can  be  calculated  from  : 


E  X  io1 


(104) 


in  which  Nc  =  number  of  armature  conductors; 
E  =  E.  M.  F.  to  be  generated; 
<?2  =  volts  per   TOO  conductors   per  100  revolutions 

per   minute   and    i    megaline    per   pole,    see 

Table  XLI. ; 

JV  =  speed,  in  revolutions  per  minute; 
$  =  useful  flux  per  pole,  in  webers. 

The  average  voltage   between   adjoining   commutator-bars 
can  be  found  from 


-_=  ,s  x  N  x 


x 


..(105) 


IS2  DYNAMO-ELECTRIC  MACHINES.  [§45 

where  <?g  is  the  average  voltage  between  segments  at  100  revo- 
lutions per  minute  and  at  i  megaline  flux,  as  given  in  columns 
8  to '13  of  Table  XLI. 

45.  Formula  for  Connecting  Armature  Coils. 

a.    Connecting  Formula  and  its  Application  to  the  Different  Methods 

of  Grouping. 

A  general  formula  for  connecting  the  conductors  of  a  closed 
coil  armature  has  been  given  by  Arnold  1  as  follows: 

If  Nc  =  number  of  conductors  arranged  around  armature  core; 
n&  =  number  of  conductors  per  commutator  segment; 
n'p  —  number  of  bifurcations  of  current  in  armature; 
/z'p  =  i,  single  bifurcation,   or  2  parallel  circuits. 
«'p  =  2,  double  bifurcation,  or  4  parallel  circuits,  etc. 
«p  =  number  of  pairs  of  magnet  poles; 

y    =  "pitch,"  or  "  spacing"  of  armature  winding;  /.  ^.,  the 
numerical  step  by  which  is  to  be  advanced  in  con- 
necting the  armature  conductors; 
then  the  number  of  armature  conductors  can  be  expressed  by 

^c   =   »a    X    («p    X  y   ±    «  p)  , 

from  which  follows  the  connecting  formula  for  any  armature: 


(106) 


The  general  rule,  then,  for  connecting  any  armature  is: 

Connect  the  end  (beginning']  of  any  coil,  x,  of  the  armature  to 
the  beginning  (end)  of  the  (x  -f-  ^)th  coil. 

For  the  various  methods  of  grouping  the  armature  coils,  the 
above  formula  is  applied  as  follows: 

I.  Parallel  Grouping. — In  this  method  of  connecting  there 
are  as  many  parallel  armature  branches  as  there  are  poles,  viz. 
2  «p  circuits,  or  «p  bifurcations.  Spiral  winding,  lap  winding, 
and  wave  winding  may  be  applied: 

(i)  Spiral  Winding  and  Lap  Winding. — In  this  case  the 
multipolar  armature  is  considered  as  consisting  of  «p  bipolar 

1  E.  Arnold,  "  Die  Ankerwicklungen  der  Gleichstrom  Dynamomaschinen." 
Berlin,  1891. 


§45]  ARMATURE    WINDING.  153 

ones,  and  independently  of  the  number  of  poles,  np  =  i  and 
«'P  =  i  is  to  be  inserted  in  (106),  and  the  formula  applied  to  a 
set  of  conductors  lying  between  two  poles  of  the  same  polarity. 
(2)  Wave  Winding. — Here  the  actual  number  of  pairs  of 
poles,  «p,  and  the  actual  number  of  bifurcations,  n'p  =  np,  is  to 
be  introduced  in  (106),  and  the  formula  applied  to  the  entire 
number  of  conductors. 

II.  Series  Grouping. — This  is  characterized   by  having  but 
two  parallel  armature  circuits,  or  one  bifurcation,  no  matter 
what   the    number  of  poles  may  be;    for  series    connecting, 
therefore,  we  have  n'v  =  i. 

In  the  special  case  of  np  =  i,  bipolar  dynamos,  the  series 
connecting  is  identical  with  the  parallel  grouping,  and  the 
winding  may  be  either  a  lap  winding  (spiral  winding)  or  a 
wave  winding;  the  latter  holds  good  also  for  «p  =  2 ;  /.  e.,  for 
four-polar  machines.  For  dynamos  with  more  than  four  poles, 
«'p  >  2,  however,  series  grouping  is  only  possible  by  means  of 
wave  winding. 

III.  Series  Parallel  Grouping. — In  the  mixed   grouping  the 
number  of  bifurcations  is  greater  than   T,  and  must  be  less 
than  «p;   hence,  in  the  connecting  formula  we  have  «'p  >    i 
and  ;z'p  <  ;/p. 

In  this  case  there  are  either  several  circuits  closed  in  itself, 
with  separate  neutral  points  on  the  commutator,  or  one  single 
closed  winding  with  »'p  parallel  branches.  The  latter  is  the  case 

N 

if  y  and  — -  are  prime  to  each  other;  the  former  if  they  have  a 

^a 

common    factor;   this  factor,   then,    indicates  the  number   of 
independent  circuits. 

b.    Application  of  Connecting  Formula  to  the    Various 

Practical  Cases. 
I.   Bipolar  Armatures. 

(i)  For  any  bipolar  armature  the  number  of  pairs  of  poles,  as 
well  as  the  number  of  bifurcations  is  =  i ;  furthermore,  the 
number  of  coils  per  commutator-bar  is  usually  =  i ;  conse- 
quently 7i&  =  i,  if  in  the  connecting  formula  the  number  of 
conductors,  JVC ,  is  replaced  by  the  number  of  coils,  nc  .  For 
ordinary  bipolar  armatures,  therefore  : 

n -  i=  i,  n&  =  i,  «'p  =   i ; y  =  nc  q=  i (107) 


154  D  YNAMO-ELECTRIC  MA  CHINES.  [§  45 

(2)  If  the  number  of  commutator  segments  is  half  the  num- 
ber of  armature  coils,  /.  <?.,  two  coils  per  commutator-bar,  then 

«P  =  i,  »a  =  2,  «'P  =  1 1 y  =  ~    =F  i (108) 

II.   Multipolar  Armatures  with  Parallel  Grouping. 

(1)  By  multiplying  the   bipolar  method  of  connecting,    we 
have: 

*p  =  i,  «.  =  i,  *'P  =  i ; ^  =  ^c  =F  i (109) 

This  is  a  spiral  winding;  beginning  and  end  of  neighbor- 
ing coils  are  connected  with  each  other,  and  a  commutator 
connection  made  between  each  two  coils.  The  number  of  sets 
of  brushes  is  2  nv. 

For  multipolar  parallel  connection  and  spiral  winding  with 
but  two  sets  of  brushes,  either  nc  divisions  may  be  used  in  the 
commutator,  and  the  bars,  symmetrically  situated  with  refer- 
ence to  the  field,  cross-connected  into  groups  of  ;/p  bars  each, 

or  only  — -  segments  may  be  employed,  and  ;zp  coils  of  same 

relative  position  to  the  poles  connected  to  each  bar  by  means 
of  «p  separate  connection  wires. 

(2)  In  connecting  after  the  wave  fashion  by  joining  coils  of 
similar  positions  in  different  fields  to  the  same  commutator 
segments,  the  following  formula  is  obtained: 

y=~ («c  T  «P)  =  ^=FI (110) 

If  y  and  nc  have  a  common  factor,  this  method  of  connecting 
furnishes  several  distinct  circuits  closed  in  itself,  the  common 
factor  indicating  their  number. 

(3)  If  tfp  similarly   situated  coils   are    connected    in   series 

between  each  two  consecutive  commutator  bars,  only  —  seg- 
ments, but  2  «p  sets  of  brushes  are  needed;  the  winding  is  of 
the  wave  type,  and  the  connecting  formula  becomes: 


§46]  ARMATURE    WINDING.  155 

III.   Multipolar  Armatures  with  Series  Grouping. 

(1)  If  all  symmetrically  situated  coils  exposed  to  the  same 
polarity,  by  joining  the  commutator  segments  into  groups^of 
ftp  bars  each,  are  connected  to  each  other,  they  can  be  consid- 
ered as  one  single  coil,  and  we  obtain: 

»P  =  #P,  «a  =  i»  »'p  =  i;  — y=  --  («c  =F  i) (112) 

np 

Each  brush,  in  this  case,  short  circuits  ftp  coils  simultaneously. 
The  same  formula  holds  good,  if  beginning  and  end  of  every 
coil  are  connected  to  a  commutator-bar  each.  The  latter  can 
always  be  done  if  ftp  is  an  uneven  number;  but  if  ftp  is  even,  the 
number  of  coils,  ftc,  must  be  odd.  In  the  case  of  ftp  uneven,  if 
ftc  is  even,  the  brushes  embrace  an  angle  of  180°;  but  if  nc  is 

odd,  an  angle  of  only  -    -  is  inclosed  by  the  brushes, 
ftp 

(2)  Instead  of  cross-connecting  the  commutator,  the  wind- 
ing itself  can  be  so  arranged  that  only  —  bars  are  required.    In 
this  case  the  connections  have  to  be  made  by  the  formula: 


ft'p  =  i;  ----  y  —  -L   f-22  q=  i  )  . 

np   \  nP         / 


ftp  =  «p,  fta  =  ftp,  ft'p  =  i;  ----  y  —  -       f-2  q=  i      .     (113) 

np   \  nP         / 

NOTE.  —  In  drum  armatures  the  beginning  and  end  of  a  coil 
being   situated    in   different   portions    of   the    circumference, 
they  should  be  numbered  alike,  and  yet  marked  differently,  in 
order  to   facilitate  the  application   of  the    above  connecting 
formulae.       By   designating    the   beginnings   of   the    coils   by 
i,  2,  3,  .  .  ......  ,  and  the  ends  by  i',  2',  3',  ........  ,  this  dis- 

tinction is  attained. 

46.  Armature  Winding  Data. 

a.  Series  Windings  for  Multipolar  Machines. 
While  a  parallel  winding  for  a  multipolar  armature  is  always 
possible  if  the  number  of  coils  is  even,  the  possibility  of  a 
series  winding  depends  upon  the  relation  between  the  number 
of  poles  and  the  number  of  conductors  per  armature  division, 
or  the  number  of  conductors  per  slot  in  case  of  a  toothed  or 
perforated  armature,  respectively.  In  the  following  Table 
XLII.,  which  is  compiled  from  data  contained  in  Parshall  and 


156 


DYNAMO-ELECTRIC  MACHINES. 


[§46 


Hobart's  work,1  the  various  kinds  of  series  windings  possible 
for  different  cases  are  given,  the  symbols  shown  in  Table  XL., 
§  44,  being  employed: 

TABLE  XLIL — KINDS  OF  SERIES  WINDINGS  POSSIBLE  FOR  MULTIPOLAR 

MACHINES. 


onductors 

per 
Armature 

Division 
or  per  Slot) 


Kind 

of 

Series 
Winding 


SERIES    WIND.INGS 
possible  for  various  numbers  of  Poles 


Poles 


Poles 


8 
Poles 


10 
Poles 


12 
Poles 


14 
Poles 


16 
Poles 


Simplex 


Duplex 


(§& 


(§& 


© 


© 


&& 


&& 


Triplex 


QQfi) 


(§© 


2 


Simplex 


Duplex 


GD© 


<§s 


sa 


© 


GD 


Triplex 


<£&& 


&& 


4 


Simplex 


Duplex 


GD© 


CD  © 


a© 


©© 


©© 


a© 


Triple 


©©© 


(§© 


6 


Simplex 


Duplex 


GD 


o 
© 


© 


o 

© 


(§© 


Triplex 


(§© 


8 


Simplex 


Duplex 


GD© 


Q© 


Q© 


Triplex 


10 


Simplex 


Duplex 


c§© 


G?© 


<§& 


cS© 


Triplex 


© 


GD 


12 


Simplex 


Duple 


Q© 


GD© 


Triple 


©o&© 


© 


GD 


14 


Simplex 


Duplex 


© 


o 
© 


C§© 


(§© 


Triplex 


$>& 


16 


Simplex 


Duplex 


©© 


GD© 


GD© 


Triplex 


°  —  Singly  reentrant  Simplex  Winding 

••  "  Duplex 

=  Doubly         ••  .. 

=  Triply          "  Triplex          •< 


1  "Armature  Windings  for  Electric  Machines,"  H.  F.   Parshall  and  H.  M, 
Hobart,  New  York,  1895. 


§46] 


ARMATURE    WINDING. 


'57 


b.    Qualification  of  Number  of  Conductors  for  the   Various 
Windings. 

The  approximate  number  of  conductors  for  the  generation 
of  a  certain  E.  M.  F.  being  calculated  from  formula  (104)  and 
Table  XXXIX.,  it  is  important  to  find  the  accurate  number 
which  is  qualified  to  give  correct  connections  for  the  desired 
kind  of  winding.  In  the  following,  practical  rules  and  a  num- 
ber of  tables  are  given  for  the  various  cases. 

(i)  Simplex  Series  Windings. — Simplex  series  windings  may 
be  arranged  either  so  that  coils  in  adjacent  fields •,  or  so  that 
coils  in  fields  of  same  polarity  are  connected  to  each  other.  In 


Fig.  99. — Short  Connection 
Type  Series  Winding. 


Fig.  100. — Long  Connection 
Type  Series  Winding. 


the  former  case,  which  is  sometimes  called  the  short  connection 
type  of  series  winding,  each  of  the  two  armature  circuits  is 
influenced  by  all  the  poles;  in  the  latter  case,  which  is  similarly 
styled  the  long  connection  type  of  series  winding,  each  circuit  is 
controlled  by  only  half  the  number  of  poles.  In  the  former, 
therefore,  the  E.  M.  Fs.  of  the  two  circuits  are-always  equal, 
in  the  latter  only  then  when  the  sum  of  all  the  lines  of  one 
polarity  is  equal  to  that  of  the  other;  a  condition  which,  how- 
ever, is  fulfilled  in  all  well  designed  machines. 

In  Fig.  99  a  winding  of  the  first  kind,  and  in  Fig.  100  one  of 
the  second  kind  is  shown. 

The  formula  controlling  simple  series  windings  is: 

Nc  —  2  (npy  ±  i),  for  drum  armatures, 
and     nc   =    np y  ±  i  ,       for  ring  armatures; 
in  which: 


IS8  DYNAMO-ELECTRIC  MACHINES.  [§46 

NQ  =  number  of  conductors; 

nc  =  number  of  coils; 

np  =  number  of  pairs  of  poles; 

y     =  average  pitch. 

While  for  the  short  connection  type  there  are  as  many  com- 
mutator segments  as  there  are  coils,  in  a  ring  armature,  or  half 
as  many  as  there  are  conductors,  in  a  drum  armature,  the 
number  of  commutator-bars  for  the  long  connection  type  of 
series  winding  is  «  ±  i 

«P 

It  is  preferable  to  have  the  pitchy  the  same  at  both  end's,  in 
order  to  have  all  end  connections  of  same  length,  but  the 
number  of  conductors  is  less  restricted  (when  np  >  2),  if  the 
front  and  back  pitches  differ  by  2.  Each  pitch  must  be  an 
odd  number,  so,  in  order  that  the  winding  passes  through  all 
conductors  before  returning  upon  itself,  it  must  pass  alter- 
nately through  odd  and  even  numbered  conductors.  Also 
when  the  bars,  as  is  usually  the  case,  occupy  two  layers,  it  is 
necessary  to  connect  from  a  conductor  of  the  upper  to  one  of 
the  lower  layer,  so  as  to  obviate  interference  in  the  position  of 
the  spiral  end  connections. 

The  folio  wing  Table  XLIIL,  page  159,  gives  formulae  for  the 
number  of  conductors  for  which  simplex  series  windings  are 
possible  in  various  cases,  and  also  gives  the  pitches  for  prop- 
erly connecting  the  conductors  among  each  other.  The 
formulae  given  refer  to  drum  armatures,  but  can  be  used  for 
ring  armatures  by  replacing  in  every  case  half  the  number  of 
conductors, 


by  the  number  of  coils,  nc. 

Example,  showing  use  of  Table  XLIII.  :  A  6-pole  simplex 
series-wound  drum  armature  is  to  yield  1.25  volt  of  E.  M.  F.  at 
3,000  revolutions  per  minute,  with  a  flux  of  27,000  webers  per 
pole.  How  many  conductors  are  required,  and  how  are  they 
to  be  connected? 

From  (104)  and  Table  XLI.  we  have 
N     _  1.25  x  io10 

"5.X  3>°°°  X  27,000 
and  Table  XLIII.  shows  that  the  number  of  conductors  in  this 


46] 


ARMATURE    WINDING. 


159 


TABLE  XLIIL—  NUMBER  OF  CONDUCTORS  AND  CONNECTING  PITCHES 
FOR  SIMPLEX  SERIES  DRUM  WINDINGS. 


I 

QUALIFICATION 
OF  NUMBER  OP  CONDUCTORS,  JV"C. 

-i- 

•M- 

w 

Jjf 

£ 

B      ' 

i 

§ 

g 

& 

S 

Equation 

Degree 
of 

Description. 

t3          1 

for  J\/c 

Evenness. 

2 

< 

i 

<i 

fc 

m 

JV 

2' 

Nc=2x±2 

Nc  even 

Any  even  number  not 
divisible  by  3. 

y~~"  1 

^ 
2/' 

^ 
2/' 

Any  singly  even  num- 

l/-ZVc     "\ 

y 

2/ 

4 

JVc=4a  ±  2 

Todd 

ber,  i.  e.,  any  odd 
multiple  of  2. 

tflU^j 

y'-l 

y'+i 

6 

«*, 

NQ  even 

Any  even  number  not 
a  multiple  of  3. 

^(f-) 

y>  ^ 

y'+i 

8 

jUt.*i 

f  odd 

Any  singly  even  num- 
ber. 

^(f*1) 

*•-! 

/+l 

Any    even    number, 

having  either  2  or 

10 

y.=ito±8 

Nc  even 

3      as      remainder 
when  divided  by  5, 
i.   e.,   any  number 

-l(f-) 

/-I 

y'+i 

having  a  2  or  an  8 

as  the  unit  digit. 

12 

*.u.*. 

^codd 

Any  singly  even  num- 
ber    not    divisible 
by  3. 

H(f^) 

y 

y'  —  \ 

y 
y'+i 

Any     even     number 

14 

*.=ite±9 

^TC  even 

having  either  2  or 
5  as  remainder 
when  divided  by  7. 

^-Kf*1) 

y'-\ 

y 

y'+i 

Any  singly  even  num- 

16 

*=lte±S 

^odd 

ber   having    either 
2  or  14  as  remain- 
der when    divided 

y=i(f±i) 

y'—l 

y 
y'+i 

by  16. 

*  General  formula:    Nc  =  -2  n    x  ±  2  ;   zn-  =  number  of  poles,  x  =  any  integer. 

t  For  ring  armatures  replace '•  by  nc  (number  of  coils). 

t  The  front  and  back  pitches  must  always  be  odd  numbers.  If  the  average  pitch,  y,  is 
odd,  both  the  front  and  back  pitches  are  equal  to  y  ;  but  if  y  is  even,  then  the  front  pitch  is 
y  —  i,  and  the  back  pitch  =  y  -f-  i.  If  the  average  pitch  is  either  odd  (y)  or  even  (y'\  ac^ 
cording  to  whether  the  -f-  or  —  sign  in  the  formula  is  used,  then  two  connections  are  possible^ 
one  having  the  pitches  y,  y,  and  the  other  the  pitches  y'  —  i,  y'  +  i. 


1 60 


DYNAMO-ELECTRIC  MACHINES. 


[§46 


case  must  fulfill  the  condition  JVC  =  6  x  ±  2,  which,  for  #  z=  5, 
and  for  the  +  sign  makes 

^"c  =  30  +  2  =  32  . 
The  same  table  gives  the  average  pitch 


from  which  follows  that  at  both  ends  of  the  armature  each 
conductor  is  to  be  connected  to  the  sixth  following  (see 
Fig.  99,  page  157). 

(2)  Multiplex  Series  Windings. — In  case  of  multiplex  series 
drum  windings  the  number  of  conductors  must  be 
^c  =  2  («p  y  ±  »m) , 

TABLE  XLIV. — NUMBER  OP  CONDUCTORS  AND  CONNECTING  PITCHES  FOR  DUPLEX 

SERIES  DRUM  WINDINGS. 


NUMBER  OP  POLES 
2np 

KIND  OF 
SERIES  WINDING.* 

QUALIFICATION 
OF  NUMBER  OF  CONDUCTORS,  _ZVc 

AVERAGE 
PITCH.  % 

FRONT  PITCH.§ 

eoe 

Equation 

Degree 
of 
Evenness. 

Description. 

2 

0  0 

iVc=4  x  ±  2 

**°-  odd 

Any  singly  even  num- 
ber. 

^=§-±2 

y 
y' 

y 

(5>C5> 

iVc=4  x  ±  4 

^even 

Any  multiple  of  4. 

»=ir±  2 

lr-\ 

y+i 

4 

O  O 

Nc=Sx 

~Te 

Any  multiple  of  8. 

y—      f     c  -[-  2  ) 

y 
y' 

y1 

<S>(2) 

2VC=8  x  ±  4 

WL  odd 
4 

Any  quadruple  of  an 
odd  integer. 

H(4-*> 

I--* 

y  ~T"1 
y'-j-l 

6 

0  0 

^c=12  z  ±  2 

^.odd 

Any  singly  even  num- 
ber, not  divisible  by  3. 

-l(f-) 

, 

w  —  I—  \ 

cs^ 

iVc=12  a;  ±  4 

f- 

Any  multiply  even 
number  (even  multi- 
ple of  2)  not  divisi- 
ble by  3. 

8 

0  0 

-ZVc=16  a;  ±  4 

±^-  odd 
4 

Any  quadruple  of  an 
odd  integer. 

r=i(f^ 

/-i 

y'  ~~  1 

§46] 


ARMATURE    WINDING. 


161 


TABLE  XLIV.— NUMBER  OF  CONDUCTORS  AND  CONNECTING  PITCHES  FOR  DUPLEX 
SERIES  DRUM  WINDINGS. — Continued. 


NUMBER  OP  POLES. 
.  2np. 

KIND  OF 
SERIES  WINDING.* 

QUALIFICATION 
OF  NUMBER  OF  CONDUCTORS,  JVC 

AVERAGE 

PiTCH.J 

FRONT  PITCH.§ 

an 

Equation 
for.Vc.t 

Degree 
of 
Evenness. 

Description. 

10 

0  0 

^=30  *  ±  6 

T  °dd 

Any  singly  even  num- 
ber having  a  4  or  a  6 
as  its  unit  digit. 

y           1(**±2\ 

y 

y 

(2)  (5) 

\NC=2Q  x  ±  4 

^.even 

Any  multiply  even 
number  having  a  4  or 
a  6  as  its  unit  digit. 

y     5  1  2    ±(V 

y'-iL/'+i 

12 

0  0 

Lar«=S4  x±s 

^even 

Any  multiple  of  8,  not 
divisible  by  3. 

1(Nc  +2\ 

y 

y 

<£><£) 

JVC=24  x  ±  4 

^  odd 

Any  quadruple  of  an 
odd  integer,  not  di- 
visible by  3. 

y      Q\  2    ±2J 

y'-i 

»'+i 

14 

O  O 
<£>® 

Nc=2Sx  ±  10 

JVC=28  *  ±  4 
JVc=32z  ±  12 

%•«" 

Any  singly  even  num- 
ber having  3  or  4  as 
remainder  when  di- 
vided by  7. 

y-l(Nc  ±2} 

y 

y 

^even 

Any  multiply  even 
number  having  3  or 
4  as  remainder  when 
divided  by  7. 

y    7|k  2  ±&) 

y'7i 

y'+i 
y 

16 

0  0 

^Lodd 

Any  quadruple  of  an 
odd  integer  of  the 
form  8  x  ±  3. 

v     1(Nc+2\ 

y 

(5)  (5) 

^.=32  *  ±  4 

Todd 

Any  quadruple  of  an 
odd  integer  of  the 
form  8  x  ±  1. 

y   s(  2  ±2J 

y'-i 

y'+i 

*  O  O  ~  singly  re-entrant  duplex  winding  "Q)  (J)  ^  doubly  re-entrant  duplex  winding. 
t  General  formula  for  O  O  :     Nc  =  4  «p  -*"  ±  (2  «p  —  4;   (  2  «p  =  number  of  poles. 
General  formula  for(5}(jLX     -We  =  4  »p  •*•  ±  4-  )  x  =  any  integer. 

^.  In  case  of  ring  windings  replace  —  —  -  by  «c  (number  of  coils). 


§  If  y  is  odd  both  pitches  are  =  y;  \iy  is  «/<?#,  the  pitches  are  y  —  i  and  jj/  +  i  ;  if  the  average  pitch  has    two 
ifferent  odd  values,  y  and  yf,  the  pitches  may  be  either  y,y*  or  y'^y';   if  the  average   pitch  is   either  odd  O')    or 
he  pitches  may  be  either^/,  y,  or  y'  —  i,  yf  -\-  i,  respectively. 


d 
even 


and  for  ring  windings  the  number  of  coils 

»c  =  n^  y  ±  nm, 

in  which  nm  is  the  number  of  multiplex  windings.  The  great- 
est common  factor  of  y  and  nm  indicates  the  number  of  re- 
entrancies.  In  Tables  XLIV.  and  XLV.,  pages  160  to  163,  data 
for  duplex  and  triplex  series  windings,  respectively,  are  given. 


162 


D  YNA MO-ELECTRIC  MA  CHINES. 


[§46 


Example:  The  flux  of  a  lo-pole  dynamo  is  8  megalines  per 
pole.  It  is  to  give  145  volts  at  125  revolutions  per  minute, 
with  a  triplex  series  drum  winding.  To  find  the  number  of 
conductors  and  the  winding  pitches. 

The  approximate  number  of  conductors  is,  by  (104): 

N  -  '*5  X  io10 

2.778  X  125  X  8,000,000 

TABLE  XLV. — NUMBER  OF  CONDUCTORS  AND  CONNECTING  PITCHES  FOR  TRIPLEX 

SERIES  DRUM  WINDINGS. 


NUMBER  OF  POLES. 
2  wp. 

KIND  OF 
SERIES  WINDING.* 

QUALIFICATION 
or  NUMBER  OF  CONDUCTORS,  Nc. 

i  • 
AVERAGE 

PlTCH.f 

fi 

M 

g 

Equation 
for  ^Tc.t 

Degree 
of 
Evenness 

Description. 

2 

000 

^c=  6  x  ±  2 

Nc  even 

Any  even  number,  not 
a  multiple  of  3. 

11                          4-    3 

y'-i 

/+! 

<d<a><a> 

Nc=  6  x  ±  6 

Nc  even 

Any  multiple  of  6. 

y  ~      2    : 

/-i 

/+! 

4 

ooo 

^Tc=12  x  ±  2 

t- 

Any  singly  even  num- 
ber, not  a  multiple  of 
3. 

'4(4+«) 

y 

,'+1 

aM 

^c=12  x  ±  6 

f-«" 

Any  odd  multiple  of  6. 

H(f  +3) 

I 

J+l 

6 

ooo 

JTe=18* 

Nc  even 

Any  multiple  of  18. 

'=-s(j+8) 

y'-l 

^+1 

ooo 

-ZVc=18  x  ±  6 

K  even 

Any  even  multiple  of  3, 

/-I 

/+! 

-8 

OOO 

Nc=24:  x  ±  1Q 

*   odd 

Any  singly  even  num- 
ber, not  a  multiple 
of  3. 

1  p 

y'-\ 

,4! 

eM 

Nc=24  x  ±  6 

f  odd 

Any  odd  multiple  of  6. 

4\  2        / 

y 

A* 

10 

000 

±  14 

Nc  even 

Any  even  number  not 
divisible  by  3,  and 
having  either  a  4  or 
a  6  as  unit  digit. 

^         . 

y 

A 

©fflffl 

JVC=30  x  ±  6 

Nc  even 

Any  odd  multiple  of  6, 
having  either  a  4  or 
a  6  as  unit  digit. 

y 
/-i 

A 

§46] 


ARMATURE    WINDING. 


163 


TABLE  XLV. — NUMBER  OF  CONDUCTORS  AND  CONNECTING  PITCHES  FOR  TRIPLEX 
SERIES  DRUM  WINDINGS. — Continued. 


« 

» 

QUALIFICATION 

— 

o 

g 

OF  NUMBER  OF  CONDUCTORS,  JVC. 

i 

too 

§  ft 

°£ 

AVERAGE 

£ 

g 

P 

PITCH4 

PH 

9 
p 

£§ 

Equation 
for  Ac.t 

Degree 
of 
Evenness. 

Description. 

1 

I 

02 

12 

000 

jVc=36  #  ±  18 

IT  odd 

Any  odd  multiple   of 
18. 

H(lT+3) 

f-i 

3/'+l 

o  o  o 

JVC=36  a?  ±  6 

-j=r-  odd 

Any  odd  multiple  of  6, 
not  divisible  by  9. 

y  =1(^-3) 

/-i 

Al 

Any  even  number,  not 

,            Q 

a  multiple  of  3,  hav- 

y 

y 

14 

000 

'l  ±22 

j>Tc  even 

ing  either  1  or  6  as 
remainder  when  di- 
vided by  7. 

y=if^.±8) 

y'-i 

y'-M 

Any  multiple  of  6,  hav- 

TV            / 

y 

V 

©  (5)  ® 

Nc=42  x  ±  6 

Nc  even 

ing  either  1  or  6  as 
remainder  when  di- 

vided by  7. 

Any  singly  even  num- 

,       JQ 

^"c 

ber,  not  a  multiple  of 

y 

y 

ooo 

_ZVJ.=48  #       gg 

-3°     Odd 

3,    having   either    6 

or  10   as   remainder 

y'  —  1 

At'        \  _"| 

16 

when  divided  by  16. 

1  (Nc  ,  o\ 

Any  odd  multiple  of  6, 

y  ~  8\  IT     j 

! 

(0^65)0 

AT"       /1Q 

Nc 

having  either  6  or  10 

y 

y 

UiiU 

Q-  odd 

as    remainder   when 

divided  by  16. 

y'-i 

y+i 

*0  O  O  =  singly  re-entrant  triplex  winding  :(&XSxS>  =  triply  re-entrant  triplex  winding, 
t  General  formula  for  O  O  O  :     NG  =  6  *p  x  ±  &  »p  -  6),  or  ' 


Nc  =  6  »J  x  ±  (4  «p  -  6)';       V  2  «P  =  "umber  of  poles. 

General  formula  for(2x£)<S)  :    Nc  =  6  »p  x  ±  6.  J      ^  =  any  integer. 

%  For  ring  windings  replace  _5  by  nc  (number  of  coils). 

$If  y  is  odd,  both  pitches  are  =  y;  liy  is  even^  the  pitches  are.y  —  i  and  y  -\-  i  ;  if  the  average  pitch  is 
odd  (y),  or  even  (y),  the  pitches  may  be  either  y,  y,  or  y'  —  i,y  -f  i,  respectively. 

By  Table   XLV.,    the   number  of  conductors   qualified  for  a 
singly  re-entrant  triplex  series  drum  winding  must  be  either 

-Wc  =  30  x  ±  4,  or  Nc  =  30  x  ±  14  , 

the  latter  of  which,  for  x  =  17,  when  using  the  -j-  sign,  fur- 
nishes the  nearest  number, 


c  =  3°  X  17  +  14  =  524 


l64  DYNAMO-ELECJ^RIC  MACHINES.  [§46 

for  which  a  singly  re-entrant  triplex  winding  is  possible.     The 
average  pitch, 

I      /C24  \ 

=  53, 

being  odd,  the  front  and  back  pitches  are  equal,  both  being 
the  same  as  the  average  pitch. 

If  a  triply  re-entrant  triplex  winding  were  desired  the  num- 
ber of  conductors  would  have  to  be  determined  from 

NG  =  30  x  ±  6  ; 
and  the  two  nearest  numbers  that  fulfill  this  equation  are 

Nc  =  30  x   17  +  6  =  516, 
and 

JVC  =  30  x  18  -  6  =  534  . 

According  to  whether  the  former  or  the  latter  number  of  con- 
ductors is  chosen,  the  average  pitch  will  be  either 

=  51, 

*\  z  / 

or 


respectively.  In  the  former  case  both  pitches  are  y  —  51;  in 
the  latter  case,  however,  the  front  pitch  has  to  be  taken 
y  —  i  =  53,  and  the  back  pitchy  -f-  i  =  55- 

(3)  Simplex  Parallel  Windings. — For  simplex  parallel  wind- 
ings there  may  be  any  even  number  of  conductors,  except  that 
in  toothed  and  perforated  armatures  the  number  of  conductors 
must  also  be  a  multiple  of  the  number  of  conductors  per  slot. 
If  it  is  desired  to  have  exactly  the  same  number  of  coils  in 
each  of  the  parallel  branches,  the  number  of  coils  must  further 
be  a  multiple  of  the  number  of  poles. 

The  pitches  in  parallel  windings  are  alternately  forward 
and  backward,  instead  of  being  always  forward,  as  in  the  series 
windings.  The  front  and  back  pitches  must  both  be  odd,  and 
should  preferably  differ  by  2 ;  therefore,  the  average  pitch 


§46] 


ARMATURE    WINDING. 


165 


should  be  even.     The  average  pitch  should  not  be  very  much 
different  from  the  number  of  conductors  per  pole, 


For  drum  fashioned  ring  windings,  or  "chord"  windings,  the 
average  pitch,  yt  should  preferably  be  smaller  than 


and  should  differ  from  it  by  as  great  an  amount  as  other  con 
ditions  will  permit. 


Fig.  101. — Simplex  Parallel  Ring  Winding. 

Fig.  10 1  shows  a  simplex  parallel  ring  winding  for  4  poles 
and  16  coils.     The  average  pitch  is 


=  4, 


consequently  the  front  pitch,  y  —  i  =  3,  and  the  back  pitch 

^+i=5- 

(4)  Multiplex  Parallel  Windings. — In  multiplex  parallel  wind- 
ings the  number  of  conductors,  Noy  must  be  even.  The  con- 
necting pitches  must  be  odd.  If  the  front  pitch  is  —  y't  then 
the  back  pitch  is  =  —  (/  -j-  2  «m),  where  nm  =  number  of  mul- 
tiple windings.  The  number  of  conductors  (^\7C),  the  average 
pitch  (y)  and  the  number  of  poles  (2  «p)  should  be  so  chosen 
that  2  «p  =  y  is  somewhere  nearly  =  N&  preferably  a  little 
smaller  than  Nf. 


i66  DYNAMO-ELECTRIC  MACHINES.  [§46 

The  greatest  common  factor  of 

#i 

™;  and  *m 

indicates  the  number  of  re-entrancies  of  the  windings.     If  the 
number  of  conductors  per  pole, 


is  not  divisible  by  the  number  of  multiple  windings,  nm,  there 
will  be  a  singly  re-entrant  winding;  and  if  it  is  divisible  by 


Fig.  102. — Duplex  Parallel  Drum  Winding. 

»m,  there  will  be  a  doubly  re-entrant  winding  in  case  of  nm  —  2 
(duplex  winding),  and  a  triply  re-entrant  winding  in  case  of 
nm  =  3  (triplex  winding). 

The  winding  pitches  for  multiple  parallel  windings  are: 


Average  pitch  y    =  -  -  x  |  -  2   ± 

Front  pitch 
Back  pitch 


=  y  —  «m, 
=  y  +  »m- 


In  case  of  a  duplex  parallel  winding/  should  be  chosen  an  odd 
number,  so  as  to  make/  —  2  and  y  -\-  2  odd  numbers  also;  and 
in  case  of  a  triplex  parallel  winding  the  average  pitch  should 
be  taken  even,  in  order  to  make  the  connecting  pitches,  y  —  3 
and/  -j-  3»  °dd- 

In  Fig.  102  a  singly  re-entrant  multiplex  parallel  winding  is 


§46]  ARMATURE    WINDING,  167 

given  for  np  —  2,  n'p  =  2,  nm  =  2,  and  Nc  =  28.     The  pitches 
in  this  case  are 

y  =  '-I  —  ±  ^ )  =  7 ; 


1/28  \ 

}    =    -I  ±    2  ) 

2V2     / 


y  —  2  —  s>  and  y  +  2  =  9  • 

There  are  two  independent  singly  re-entrant  windings,  each 
having  4  parallel  branches,  making  8  paths  altogether;  6  of 
these  paths  contain  4  conductors  each,  and  the  remaining  2 
but  2  conductors  each.  In  order  to  have  an  equal  number  of 
conductors  in  all  branches,  Nc  must  be  a  multiple  of  2  «'p  x  «m, 
or  in  the  present  example  the  number  of  conductors  should  be 
either  24  or  32;  in  the  former  case  each  of  the  8  parallel 
branches  would  have  3,  and  in  the  latter  case  4,  conductors. 

As  further  illustrations  of  the  rules  given  above  we  take 
(i)  Nc  —  486,  np  =  3,  n'p  —  3,  nm  =  2;  this  is  a  6-pole  duplex 
parallel  winding;  since 

Nc         486  _ 

,      '      O  I 

2  np  6 

is  not  divisible  by  nm  —  2,  we  have  a  singly  re-entrant  duplex 
winding  (oo),  for  which  the  pitches  are: 


y  _  2  =  79j  and  v  +  2  =  83  . 

(2)  Nc  —  1,368,    »p  =  6,  «'p  =  6,  «m  =  3;  in  this  case,  which 
represents  a  triplex  parallel  winding  for  12  poles, 


2tfp  12 

is  a  multiple  of  «m  =  3,  and  therefore  we  have  a  triply  re- 
entrant triplex  winding  (  (@)(^)(g)  );  the  average  pitch  for  this 
winding  is 

r    A,  368    ,     \ 
^  =  6(     2      ±3J-H4; 

hence  the  front  and  back  pitches  are 

y  -  3  =  in,  and  y  +  3  =  117, 
respectively. 


CHAPTER  IX. 

DIMENSIONING    OF    COMMUTATORS,   BRUSHES.   AND    CURRENT- 
CONVEYING    PARTS    OF    DYNAMO. 

47.   Diameter  and  Length  of  Commutator  Brush  Sur- 
face. 

In  small  and  medium-sized  machines  the  commutator  is  usu- 
ally placed  upon  the  shaft  concentric  with  the  armature,  and 
has  the  collecting  brushes  sliding  upon  its  peripheral  surface. 
In  large  ring  dynamos  the  armature  winding  is  often  performed 
by  means  of  bare  copper  bars,  and  the  current  is  then  taken  off 
directly  from  the  winding;  thus,  in  the  Siemens  Innerpole  dy- 
namo the  brushes  rest  upon  the  external  periphery  of  the  arma- 
ture, and  in  the  Edison  Radial  Outerpole  machine  the  two 
end  surfaces  of  the  armature  are  formed  into  commutators. 
If  it  is  not  convenient  to  use  part  of  the  armature  winding 
itself  as  the  commutator,  in  large  diameter  machines  it  is  of 
advantage  to  provide  a  separate  face-commutator,  that  is,  a 
commutator  with  the  brush  surface  perpendicular  to  the  arma- 
ture shaft;  for  in  this  case  the  otherwise  unavailable  space 
between  the  armature  periphery  and  the  shaft  is  made  use  of, 
and  a  saving  in  length  of  machine  and  in  weight  will  be 
effected. 

For  the  peripheral  as  well  as  for  the  face  type  commutator 
the  same  principles  of  construction  hold  good;  the  only  differ- 
ence is  that  in  the  latter  case  the  outer  diameter  of  the  brush 
surface  is  fixed  by  the  external  diameter  of  the  armature,  and 
that  therewith  the  top  width  of  the  bars  is  directly  given  by 
the  number  of  commutator  divisions,  while  in  the  former  case 
the  dimensions  of  the  brush  surface  can  be  chosen  between 
comparatively  much  wider  limits. 

In  low  potential  machines  with  small  number  of  divisions, 
the  thickness  of  the  substructure  determines  the  diameter  of 
the  commutator;  in  high  potential  machines,  however,  espe- 
cially those  of  multipolar  type,  where  the  number  of  commuta- 


§47]    COMMUTATORS,  BRUSHES,  AND   CONNECTIONS.      169 

tor  segments  is  very  great,  the  width,  at  top,  of  the  commu- 
tator bars,  their  number,  and  the  thickness  of  the  insulation 
between  them  fix  the  outside  diameter. 

The  bars  must  be  large  enough  in  cross-section  to  carry  the 
whole  current  generated  in  the  armature  without  undue  heat- 
ing, and  shall  continue  so  after  a  reasonable  amount  of  wear. 
They  must  be  of  sufficient  length  to  allow  a  proper  number  of 
brushes  to  take  off  the  current. 

The  same  brush  contact  surface  may  be  obtained  by  employ- 
ing either  a  broad  thin  brush  on  a  small  diameter  commutator, 
or  a  narrow  thick  one  on  a  large  diameter,  the  number  of  bars 
being  the  same  in  both  cases,  their  width,  consequently,  larger 
in  the  latter  case.  With  larger  diameter  and  greater  conse- 
quent peripheral  velocity  there  will  be  more  wear  of  both 
brushes  and  segments,  and  greater  consumption  of  energy  due 
to  the  increased  friction  of  the  brushes. 

The  segments  are  usually  made  of  copper  (cast,  rolled,  or 
forged),  phosphor  bronze,  or  gun  metal,  sometimes  brass,  and 
even  iron  being  used;  the  materials  for  the  substructure  are 
phosphor  bronze,  brass,  or  cast  iron. 

From  all  this  it  will  be  obvious  that  a  general  formula  for  the 
diameter  of  the  commutator  cannot  be  established,  and  that, 
on  the  contrary,  this  dimension  has  to  be  properly  chosen  in 
every  case  with  reference  to  the  armature  diameter  to  the 
design  of  the  commutator,  to  the  materials  employed,  to  the 
strength  of  the  substructure,  or  the  thickness  of  the  bar, 
respectively,  and,  finally,  with  reference  to  the  wear  of  the 
segments. 

The  commutator  diameter  being  decided  upon,  the  size  of 
the  brushes  can  now  be  calculated,  as  shown  in  §  49,  and, 
from  this,  the  length  of  the  commutator  can  be  found. 

In  order  to  prevent  annular  grooves  being  cut  around  the 
commutator,  the  brushes  ought  to  be  so  adjusted  that  the 
gaps  between  those  in  one  set  do  not  come  opposite  the  gaps 
in  the  other  set.  Denoting,  Fig.  103,  the  width  of  each  brush 
by  <£b,  their  number  per  set  by  «b,  and  the  gap  between  them 
by  /'b ,  we  consequently  obtain  the  total  length  of  the  commu- 
tator brush  surface  from: 

(*b+/b)    •  "(114) 


1 70  DYNAMO-ELECTRIC  MACHINES.  [£48 

This  length  of  brush  surface  should  be  available  even  after 
the  commutator  has  been  turned  down  to  its  final  diameter;  the 
original  diameter  must  therefore  have  a  somewhat  larger  con- 


— /c H 

Fig.  103. — Arrangement  of  Commutator  Brushes. 

tact  length.     An  addition  to  /c  of  from  ^  to  i  inch,  according 
to  the  depth  of  the  bar,  is  thus  necessitated. 

As  to  the  practical  design  of  commutators,  while  the  same 
general  plan  is  followed  in  all,  the  details  of  construction  are 
almost  numberless.  Structural  cross-sections  and  descriptions 
of  the  commutators  manufactured  by  the  Electron  Manufac- 
turing Company,  the  Storey  Motor  and  Tool  Company,  the 
Royal  Electric  Company,  the  Fort  Wayne  Electric  Corpora- 
tion, Paterson  &  Cooper,  the  Giilcher  Company,  the  General 
Electric  Company,  the  Triumph  Electric  Company,  the  Sie- 
mens &  Halske  Electric  Company,  the  Walker  Company,  and 
others,  are  given  in  an  article  *  in  American  Electrician. 

48.  Commutator  Insulations. 

In  a  commutator  the  insulation  has  to  form  a  part  of  the 
general  structure,  and  has  to  take  strain  in  common  with 
other  material  used;  from  its  natural  cleavage  and  hardness, 
therefore,  mica  is  particularly  suitable  for  commutator  insula- 
tions, and  is,  in  fact,  almost  exclusively  used  for  this  purpose, 
only  asbestos  and  vulcanized  fibre  being  employed  in  rare 
cases. 


1  "  Modern  Commutator  Construction,"  American  Electrician^  vol.  viii.  p. 
83  (July,  1896). 


§49]     COMMUTATORS,  BRUSHES,  AND  CONNECTIONS, 


The  thickness  of  the  commutator  insulation   ought  to   be 
proportional  to  the  voltage  of  the  machine,  and,  for  the  various 


m^^^^p§§wi«^ 

Fig.   104. — Commutator  Insulations. 

positions  with  reference  to  the  bars,  see  ^{,  h\,  /i"i}  Fig.  104, 
should  be  selected  within  the  following  limits: 

TABLE  XL VI. — COMMUTATOR  INSULATIONS  FOB  VARIOUS  VOLTAGES. 


POSITION 

OP 

INSULATION. 

THICKNESS  OP  INSULATION  (MICA): 

Up  to  300  Volts. 

400  to  700  Volts. 

800  to  3,000  Volts. 

inch. 

mm. 

inch. 

mm. 

inch. 

mm. 

Side  Insulation  (hi) 
Bottom  Insulation  (h'\) 
End  Insulation  (^"i) 

.020  to   .060 

%"•% 

.5  to  .75 
1.25  "  2.5 
1.5  "  2.5 

.030  to  .040 

4  -  1 

.75  to  1 
1.5     "   3 
2.5     "   3 

.040  to   .060 
&  "  & 

£    "  A 

1      to  1.5 
2.5    "  5 

3       "  5 

49.  Dynamo  Brushes.1 

a.   Material  and  Kinds  of  Brushes. 

For  low  potential  machines  having  a  large  current  output,  it 
is  the  practice  to  employ  thick  copper  brushes,  made  up  either 
of  copper  wires,  or  copper  strips,  or  copper  wire  gauze,  in 
order  to  secure  a  large  number  of  contact  points,  and  to  set 
them  so  as  to  make  an  angle  of  about  45°  with  the  commutator 
surface,  as  shown  in  Fig.  105. 

In  small  dynamos,  often  springy  copperplates  are  used  which 
are  placed  tangentially  to  the  commutator  periphery,  as 
illustrated  in  Fig.  106. 

For  high  potential  machines,  especially  for  railway  genera- 
tors and  motors,  carbon  brushes  are  used  in  order  to  aid  in  the 
sparkless  collection  of  the  current  at  varying  load.  As  each 

1  "  Commutator  Brushes  for  Dynamo-Electric  Machines:  their  selection,  their 
proper  contact-area,  and  their  best  tension,"  by  A.  E.  Wiener,  American  Elec- 
trician, vol.  viii.  p.  152  (September,  1896). 


172 


DYNAMO-ELECTRIC  MACHINES. 


commutator  segment  enters  under  the  brush,  the  area  of  con- 
tact is,  at  first,  very  small  and,  owing  to  the  high  specific  re- 
sistance of  carbon,  a  considerable  resistance  is  offered  to  the 
passage  of  the  current  from  the  branch  of  the  armature  of 
which  that  segment  at  the  time  is  the  terminal,  into  the  exter- 
nal circuit.  This  gives  rise  to  a  considerable  local  fall  of 
potential,  which  diverts  a  comparatively  large  portion  of  the 
armature  current  through  the  neighboring  coil  into  which  it 
flows  against  the  existing  current,  causing  the  latter  to  reverse 
quickly  in  opposition  to  the  E.  M.  F.  of  self-induction,  thereby 


Fig.   105. — Sloping  Copper  Wire  (or 
leaf)  Brush. 


Fig.    106. — Tangential  Copper  Plate 
Brush. 


preparing  the  short-circuited  coil  to  join  the  successive  arma- 
ture circuit  of  opposite  polarity  without  sparking.  (Compare 
with  sections  on  sparkless  commutation  of  armature  cur- 
rent, in  §  13.)  The  resistance  of  the  carbon  brushes  cannot 
be  depended  upon  for  the  complete  commutation  of  the  entire 
current,  but  in  most  generators,  especially  in  those  with 
toothed  and  perforated  armatures,  fully  half  the  armature 
current  may  be  thus  commutated.  In  railway  generators  it 
is  usual  to  adjust  the  brushes  so  that  at  no  load  they  are  in 
the  neighborhood  of  the  forward  pole-tips  where  the  pole- 
fringe  E.  M.  Fs.  generated  are  sufficient  to  reverse  one-half 
of  the  normal  current,  the  remaining  half  being  then  taken 
care  of  by  the  brushes. 

Carbon  brushes  are  either  set  tangentially  (Fig.  107),  or 
radially  (Fig.  108),  with  respect  to  the  commutator  circumfer- 
ence, the  latter  arrangement  having  the  advantage  of  admitting 
of  reversal  of  the  rotation,  without  changing  the  brushes. 

To  use  carbon  brushes  exclusively  on  machines  of  low  volt- 
age would  be  very  bad  practice,  because  carbon  has  so  much 


§49]     COMMUTATORS,  BRUSHES,  AND  CONNECTIONS.      173 

higher  resistance  than  copper  that  the  drop  of  potential  would 
be  excessive,  and  too  great  a  percentage  of  the  power  of  the 
machine  would  be  used  up  for  commutation.  If,  therefore, 
the  resistance  of  an  ordinary  copper  brush  is  not  high  enough 


Fig.   107. — Tangential  Carbon  Brush.          Fig.  108. — Radial  Carbon  Brush. 

for  sparkless  collection,  a  copper  gauze  brush  must  be  em- 
ployed, which  has  a  much  higher  resistance  than  a  copper  leaf 
brush,  and  while  there  are  some  mechanical  advantages  in. 
using  it,  such  as  cooling  effects  and  smoother  wear  of  the 
commutator,  yet  the  principal  reason  it  stops  sparking  is  that 
it  has  a  higher  resistance.  In  case  the  resistance  is  still  too 
low,  the  next  step  is  the  application  of  a  brass  gauze  brush 
having  about  twice  the  resistance  of  copper  gauze.  If  that  is 
not  enough  yet,  some  form  of  carbon  brush  which  has  its 
resistance  reduced,  must  be  resorted  to.  Carbon  itself  cannot 
have  its  resistivity  changed,  but  by  mixing  copper  filings  with 
the  carbon  powder,  or  by  molding  layers  of  gauze  in  it,  the 
conductivity  of  the  brush  can  be  increased.  Instead  of  arti- 


COPPER 
BRUSH 


Figs.  1 09  and  no. — Combination  Copper-Carbon  Brushes. 

ficially  decreasing  the  resistance  of  carbon,  combination  brushes 
consisting  either  in  copper  brushes  provided  with  carbon  tips, 
Fig.  109,  or  in  carbon  brushes  sliding  upon  the  commutator 
and  having,  in  turn,  copper  brushes  resting  against  themselves, 
Pig.  no,  are  sometimes  employed,  and  in  case  of  very  heavy 


174 


D  YNA MO-ELECTRIC  MA  CHINES. 


[§49 


currents,  the  addition  to  each  set  of  copper  brushes,  of  a  com- 
bination brush  set  somewhat  ahead  of  the  copper  brushes  as 
shown  in  Fig.  in,  has  been  found  to  greatly  improve  the 


COMBINATION 
BRUSH 


COPPER  BRUSH 


Fig.   in. — Arrangement  of  Copper  and  Combination  Brushes  for  Collection 
of  Large  Currents. 

sparkless  running  of  the  machines.  With  the  latter  arrange- 
ment, the  tension  on  the  combination  brushes  should  exceed 
that  on  the  copper  brushes  sufficiently  to  enable  them  to  take 
their  full  share  of  the  current  as  nearly  as  possible. 

b.   Area  of  Brush  Contact. 

The  thickness  of  the  brushes,  according  to  the  current  capa- 
city of  the  machine,  to  the  grouping  of  the  armature  coils,  to 
the  material  and  kind  of  the  brush  and  fro  the  dimensions  of 
the  commutator,  varies  between  less  than  the  width  of  one  to 


Figs.  112  and  113. — Circumferential  Breadth  of  Brush  Contact. 

that  of  three  and  even  more  commutator  segments.  In  case 
the  brush  covers  not  more  than  the  width  of  one  bar,  as  in 
Fig.  112,  only  one  armature  coil  is  short-circuited  at  any  time, 


§49]     COMMUTATORS,  BRUSHES,  AND  CONNECTIONS.      175 

while  in  case  of  brushes  thicker  than  the  width  of  one  bar  plus 
two  side  insulations,  Fig.  113,  two  or  even  more  coils,  at  times, 
are  simultaneously  short-circuited  under  each  set  of  brushes_ 
The  breadth  of  the  brush  contact  surface  in  the  former  case 
(Fig.  112)  is  equal  to  the  thickness  of  the  beveled  end  of  the 
brush  measured  along  the  commutator  circumference;  in  the 
latter  case  (Fig.  113)  is  the  breadth  of  the  brush  bevel  dimin- 
ished by  the  sum  of  the  thickness  of  the  commutator  insula- 
tions covered  by  the  brush,  and  can  be  generally  expressed  by 
the  formula 

/  j   ^ ,  ^        \ 

(115) 


where  £k  =  circumferential  breadth  of  brush  contact,  in  inches; 

«k  =  number  of  commutator-bars  covered  by  the  thick- 
ness of  one  brush; 

</k  —  diameter  of  commutator,  in  inches; 

nc  =  number  of  commutator-divisions; 

hi  —  thickness  of  commutator  side-insulation,  in  inches, 
see  Table  XLVI. 

If  the  brush  covers  less  than  one  bar,  as  in  Fig.  112,  nk  is  a 
fraction;  if  the  width  of  the  brush  is  from  one  bar  to  one  bar 
plus  two  side  insulations,  nk  =  i ;  when  between  two  bars  plus 
one  insulation  and  two  bars  plus  three  insulations,  #k  =  2,  etc. ; 
and  if  the  brush  covers  from  one  bar  plus  two  insulations  to 
two  bars  plus  one  insulation,  or  from  two  bars  plus  three  insula- 
tions to  three  bars  plus  two  insulations,  etc.,  the  value  of  ;/k 
is  a  mixed  number,  consisting  of  an  integer  and  a  fraction. 

Having  decided  upon  «kand  having  calculated  £k  from  (115), 
the  width  of  the  contact  area,  and  subsequently  the  width  of 
the  brushes,  can  be  found  for  a  given  current  output  of  the 
dynamo  by  providing  contact  area  in  proportion  to  the  current 
intensity.  In  order  to  keep  the  brushes  at  a  moderate  tem- 
perature, and  the  loss  of  commutation  within  practical  limits,  the 
current  density  of  the  brush  contact  should  not  exceed  150  to 
175  amperes  per  square  inch  in  case  of  copper  brushes  (wire, 
leaf  plate,  and  gauze),  100  to  125  amperes  per  square  inch  for 
brass  gauze  brushes,  and  30  to  40  amperes  per  square  inch  in 
case  of  carbon  brushes. 


176  DYNAMO-ELECTRIC  MACHINES,  [§  *» 

Taking  the  lower  of  the  above  limits  of  the  current  densities, 
the  effective  length  of  the  brush  contact  can  consequently  be 
expressed  by 


for  copper  brushes,  by 
for  brass  brushes,  and  by 


for  carbon  brushes,  the  symbols  employed  being 

4  =  effective  length  of  brush  contact  surface,  in  inches; 
=  nb  X  ^>  («u  =  number  of  brushes  per  set,  £b  =  width  of 

brush) ; 

I  —  total  current  output  of  dynamo,  in  amperes; 
n\  =  number  of  pairs  of  brush  sets  (usually  either  n"v  =  i,  or 
equal  to  the  number  of  bifurcations  of  the  armature 
current,  n\  =  n'p). 

For  the  purpose  of  securing  a  good  contact,  the  length  /k 
should  be  subdivided  into  a  set  of  «b  individual  brushes,  of  a 
width  ^b  each,  not  exceeding  i^  to  2  inches.  In  small 
machines,  where  one  such  brush  would  suffice,  it  is  good 
practice  to  employ  two  narrow  brushes,  even  down  as  low  as 
3/8  inch  each,  in  order  to  facilitate  their  adjusting  or  exchang- 
ing while  the  machine  is  running. 

c.   Energy- Loss  in  Collecting  Armature  Current.     Determination 
of  Best  Brush  Tension. 

The  brushes  give  rise  to  two  losses  of  energy:  an  electrical 
energy-loss  due  to  overcoming  contact  resistance,  and  a  mechan- 
ical loss  caused  by  friction.  Both  of  these  losses  depend  upon 
the  pressure  with  which  the  brushes  are  resting  upon  the  com- 
mutator, the  electrical  loss  decreasing  and  the  mechanical  loss 
increasing  with  increasing  brush  tension.  There  will,  there- 
fore, in  every  single  case,  be  one  certain  pressure  per  unit 
area  of  brush  contact,  for  which  the  sum  of  the  brush  losses 
will  be  a  minimum.  With  the  object  of  determining  this  criti- 


§49]     COMMUTATORS,  BRUSHES,  AND  CONNECTIONS.      177 

cal  pressure,  E.  V..  Cox  and  H.  W.  Buck1  have  investigated 
the  influence  of  the  brush  tension  upon  the  contact  resistance 
and  upon  the  friction,  for  various  kinds  of  brushes.  They 
found  (i)  that  the  friction  increases  in  direct  proportion 


•5  1  1'5  2  2-5  3  3-5 

BRUSH  PRESSURE,  IN  POUNDS  PER  SQUARE  INCH. 


Fig.  114. — Contact  Resistance  and  Friction  per  Square  Inch  of  Brash  Surface,  on 
Copper  Commutator  (dry),  at  Peripheral  Velocity  of  1,000  Feet  per  Minute. 

with  the  tension;  (2)  that  the  contact  resistance  decreases  at 
first  very  rapidly,  but  that  beyond  a  certain  point  a  great 
increase  in  pressure  produces  only  a  slight  diminution  of 
resistance;  (3)  that  slightly  oiling  the  contact  surface,  while 
not  perceptibly  increasing  the  electrical  resistance,  greatly 


1  The  Relation  between  Pressure,  Electrical  Resistance,  and  Friction  in  Brush 
Contact,"  Electrical  Engineering  Thesis,  Columbia  College,  by  E.  V.  Cox  and 
H.  W.  Buck.  Electrical  Engineer,  vol.  xx.  p.  125  (August  7,  1895);  Electrical 
World,  vol.  xxvi.  p.  217  (August  24,  1895). 


i78 


DYNAMO-ELECTRIC  MACHINES. 


[§49 


diminishes  the  friction;  (4)  that  for  a  copper  brush  the  friction 
is  greater  and  the  contact  resistance  smaller  than  for  a  carbon 
brush  of  same  area  at  the  same  pressure;  (5)  that  the  friction 
of  a  radial  carbon  brush  is  greater  than  that  of  a  tangential 
carbon  brush  at  the  same  pressure;  (6)  that  for  the  same 
brush  both  the  contact  resistance  and  the  friction  are  consid- 
erably less  on  a  cast-iron  cylinder  than  on  a  commutator;  and 


0'51  1-5  2  2-5  3  3-5  4 

BRUSH  PRESSURE,  IN  POUNDS  PER  SQUARE  INCH. 

Fig.  115. — Contact  Resistance  and  Friction  per  Square  Inch  of  Brush  Surface, 
on  Cast-iron  Cylinder. 


(7)  that  for  all  kinds  of  brushes  the  friction  is  less  at  high  than 
at  low  peripheral  speeds,  while  the  contact  resistance  is  but 
slightly  increased  by  raising  the  velocity. 

In  Figs.  114  and  115  the  averages  of  their  results  are  plotted, 
the  former  giving  the  curves  of  contact  resistance  and  friction 
for  an  ordinary  commutator,  without  lubrication,  and  the  latter 
the  corresponding  curves  for  the  case  that  the  commutator  is 
replaced  by  a  cast-iron  cylinder. 

From  Fig.  114  the  following  Table  XLVII.  is  derived, 
which,  in  addition  to  the  data  obtained  from  the  curves,  also 


§49J     COMMUTATORS*  BRUSHES,  AND  CONNECTIONS.      179 

contains   the   brush  friction   for  the  case   the  commutator  is 
slightly  oiled: 

TABLE  XLVIL—  CONTACT  RESISTANCE  AND  FRICTION  FOR  DIFFERENT 
BRUSH  TENSIONS. 


CONTACT  RESISTANCE 

TANGENTIAL  PULL  DUE  TO  BRUSH  FRICTION 

PER  SQUARE  INCH 
OF  BRUSH  SURFACE, 

PER  SQUARE  INCH  OF  CONTACT 
AT  PERIPHERAL  SPEED  OF  1,000  FEET  PER  MINUTE. 

pk)  IN  OHM. 

yk,  IN  POUNDS. 

BRUSH    i 

IN 

POUNDS 

4 

Commutator  Dry. 

Commutator  Oiled. 

PER 

3 

-•g 

•  .3 

SQUARE 
INCH. 

!« 
P 

31 

E 

s« 

Is  a 

J 

*3 

afl 

jj 

11 

fi 

ll 

il 

in 

'  -g 

al 

«3  ;_ 
PH  £> 

H 

W| 

Is 

BO 

Ij 

|| 

&s 

58 

1§ 

a 

0 

Q 

9 

&l 

S 

St1 

H| 

J 

.5 

.010 

.50 

.40 

.6 

.3 

.5 

.16 

.10 

.15 

1 

.009 

.24 

.20 

1.15 

.63 

1 

.32 

.20 

.30 

1.5 

.008 

.15 

.13 

1.7 

.95 

1.5 

.48 

.30 

.45 

2 

.007 

.12 

.10 

2.25 

1.25 

2 

.64 

.40          .60 

2.5 

.006 

.10 

.087 

2.8 

1.6 

2.5 

.80 

.50 

.75 

3 

.0055 

.09 

.08 

3.4 

1.9 

3 

.96 

.60          .90 

3.5 

.0052 

.083 

.075 

3.95 

2.2 

3.5 

1.12 

.70        1.05 

4 

.005 

.08 

.07 

4.5 

2.5 

4 

1.30 

.80 

1.20 

The  specific  pull,  yk,  due  to  brush  friction,  in  columns  5  to 
10  of  the  above  table,  is  given  for  a  peripheral  velocity  of 
1,000  feet  per  minute;  at  2,000  feet  per  minute  it  is  7/8, 
at  3,000  feet  per  minute  3/4,  at  4,000  feet  per  minute  5/8,  and 
at  5,000  feet  per  minute  only  1/2  of  what  it  is  for  that  pres- 
sure at  1,000  feet  per  minute,  and  for  any  commutator  velocity, 
z-k,  can  be  found  from  the  formula 


......  (.19) 


From  Table  XLVII.  the  electrical  brush  loss  is  calculated  by 
dividing  the  contact  resistance  given  for  the  particular  brush 
tension  employed,  by  the  contact  area,  and  multiplying  the 


1  80  D  YNA  MO-ELECTRIC  MA  CHINES.  [§  49 

quotient  by  the  number  of  sets  of  brushes  and  by  the  square  of 
the  current  passing  through  each  set,  thus: 

*  =  2     x 


=  .00268   X         ft*  x  /2  „    horse  power,       .....  (120) 

^k    X    #k     X    72  p 

where  ./\  =  energy  absorbed  by  contact  resistance  of  brushes; 
pk  =  resistivity  of  brush  contact,  ohm  per  square  inch 

surface,  from  Table  XLVIL; 
4  x  ^k  =  contact   area  of  one  set  of   brushes,   in  square 

inches; 

#"p  =  number  of  pairs  of  brush  sets; 
/  =  current  output  of  dynamo. 

And  the  frictional  loss  is  obtained  in  multiplying  the  tan- 
gential pull,  given  for  the  respective  brush  tension  and  cor- 
rected to  the  proper  peripheral  velocity  according  to  formula 
(119),  by  the  total  brush  contact  area  and  by  the  peripheral 
velocity  of  the  commutator,  and  dividing  the  product  by 
33,000,  the  equivalent  of  one  horse  power  in  foot-pounds  per 
minute: 

p  —  A  x  2  n"p  x  4  x  ^  x  pk 

33,000 
=  6  x  io-5  X  /'k  X  4  X  ^k  X  n\  X  z>k  ,      ........  (121) 

in  which  Pt  =  energy  absorbed  by  brush  friction,  in  HP; 

/'k  =  specific  tangential   pull  due  to  friction,  at  ve- 

locity z>k,  in  pounds,  see  formula  (119); 
2  #"p  X  /k  X  <^k  —  total  area  of  brush  contact  surfaces,   in 

square  inches; 

vk  =  peripheral  velocity  of  commutator,  in  feet  per 
minute, 

_     <4  X  7t  X  N 

12 

By  calculating  the  amounts  of  /\  and  ./^  ,  from  (120)  and  (121) 
respectively,  for  different  brush  tensions,  the  best  tension 
giving  a  minimum  value  of  the  total  brush-loss,  />k  -f-  Pt  ,  can 
readily  be  found. 


§50]     COMMUTATORS,  BRUSHES,  AND  CONNECTIONS.      181 

50.  Current-Conveying  Parts. 

Care  must  also  be  exercised  in  the  proportioning  of  those 
parts  of  a  dynamo  which  serve  to  convey  the  current,- col- 
lected by  the  brushes,  to  the  external  circuit.  For,  if  mate- 
rial is  wasted  in  these,  the  cost  of  the  machine  is  unneces- 
sarily increased;  and  if,  on  the  contrary,  too  little  material  is 
used,  an  appreciable  drop  in  the  voltage  and  undue  heating 
will  be  the  result. 

In  the  design  of  such  current-conveying  parts,  among 
which  may  be  classed  brush  holders,  cables,  conductor  rods, 
cable  lugs,  binding  posts,  and  switches,  the  attention  should 


Figs.  116  to  118. — Various  Forms  of  Spring  Contacts. 


therefore  be  directed  to  the  smallest  cross-section  through 
which  the  current  has  to  pass,  and  to  the  surfaces  of  contact 
transferring  the  current  from  one  part  to  another.  The  max- 
imum permissible  current  density  in  the  cross-section,  while 
depending  in  a  small  degree  upon  the  ratio  of  circumference  to 
area  of  cross-section,  is  chiefly  determined  by  the  choice  of  the 
material;  that  in  the  area  of  contact  between  two  parts,  how- 
ever, although  the  conductivity  of  the  material  employed  is  of 
some  consequence,  depends  mainly  upon  the  condition  of  the 
contact  surfaces  and  upon  the  amount  of  pressure  that  can  be 
applied  to  the  joint. 

The  most  usual  forms  of  contact  are  those  shown  in  Figs. 
116  to  125.  Figs.  116  to  118  represent  spring  contacts  as  used 
in  switches;  in  Fig.  116  the  switchblade  is  cast  in  one  with  the 
lever,  while  in  Figs.  117  and  118  the  levers  are  provided  with 
separate  copper  blades.  The  former  is  a  single  switch  making 
and  breaking  contact  between  the  blade  and  the  clips,  the  lever 
itself  forming  the  terminal  of  one  pole;  the  latter  two  are 
double  switches,  the  connection  being  established  between  two 
sets  of  clips  by  way  of  the  blade,  when  the  switch  is  closed. 


182 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§50 


In  order  to  prevent  the  forming  of  an  arc  in  opening  a  switch, 
especially  a  double  switch,  each  blade  must  leave  all  the  clips 
with  which  it  engages  simultaneously  over  its  entire  length. 
For  this  purpose  either  the  blade,  or  the  clips,  or  both  (Figs. 
117,  118,  and  116,  respectively)  have  to  be  cut  off  at  such  an 
angle  that,  in  the  closed  position  of  the  switch,  the  enter-line 
of  the  blade  and  the  line  through  the  tops  of  the  clips  are  both 
tangents  to  the  same  circle  (shown  in  dotted  lines  in  Figs.  116 
to  1 18),  described  from  the  centre  of  the  lever  fulcrum.  If 
all  clips  are  then  made  of  equal  widths,  as  in  Fig.  117,  those 


FIG.  119.  -LAMINATED  JOINT. 


FIG.  121. -LUG  HELD  BETWEEN 

NUTS  ON  A  STUD.  F(G.  122. -LUG 'CLAMPED 

BETWEEN  WASHERS. 


FIG.  f24. -TAPER  PLUG 

INSERTED  BETWEEN 

TWO  SURFACES. 


,FIG.  125. -TAPER  PLUG 

GROUND  TO  SEAT 

AND  BOLTED. 


Figs.  119  to  125. — Various  Forms  of  Screwed,  Clamped,  and  Fitted 
Contacts. 

nearest  to  the  fulcrum,  in  case  of  a  double  switch,  have  less 
contact  area  than  the  remote  ones,  and  in  designing  such  a 
switch  this  smaller  contact  area  is  to  be  made  of  sufficient  size 
to  carry  half  the  armature  current,  if  there  is  but  one  blade, 
and  one-quarter  of  the  total  current  when  the  lever  has  two 
blades.  By  making  the  clips  near  the  fulcrum  correspondingly 
wider  than  those  at  the  other  end  of  the  blade,  as  in  Fig.  118, 
all  the  contact  surfaces  can,  however,  be  made  of  equal  area. 
Various  forms  of  screwed  or  bolted  contacts  are  shown  in 
Figs.  119,  120,  and  121;  a  clamped  contact  is  illustrated  in  Fig. 
122;  two  common  forms  of  fitted  contact  in  Figs.  123  and  124; 
and  an  excellent  fitted  and  screwed  contact  in  Fig.  125. 


§50]     COMMUTATORS,  BRUSHES,  AND   CONNECTIONS.      183 


The  permissible  current  densities  for  all  these  different 
kinds  of  contact  as  well  as  for  the  cross-section  of  different 
materials  are  compiled  in  the  following  Table  XLVIII.,  which 
more  in  particular  refers  to  the  larger  sizes  of  dynamos, 
since  in  small  machines  purely  mechanical  considerations 
lead  to  much  heavier  pieces  than  are  required  for  electrical 
'purposes: 

TABLE  XLVIII. — CURRENT  DENSITIES  FOR  VARIOUS  KINDS  OF  CONTACTS  AND  FOR 
CROSS-SECTION  OF  DIFFERENT  MATERIALS. 


KIND 

OP 

CONTACT. 

MATERIAL. 

CURRENT  DENSITY. 

ENGLISH  MEASURE. 

METRIC  MEASURE. 

Amps,  per 
square  inch. 

Square  mils 
per  amp. 

Amps, 
per  cm.2 

mm.2  per 
ampere. 

Sliding  Contact 
(Brushes) 

Copper  Brush 

150  to     175 

5,700  to    6,700 

23  to  28 

3.5  to   4.5 

Brass  Gauze  Brush 

100  to     125 

8,000  to  10,000 

15  to  20 

5    to     7 

Carbon  Brush 

30  to       40 

25,000  to  33,300 

4.5  to    6 

16    to   22 

Spring  Contact 
(Switch  Blades) 

Copper  on  Copper 

60  to       80 

12,500  to  16,700 

9  to  12.5 

8    to    11 

Composition  on  Copper 

50  to       60 

16,700  to  20,000 

7.5  to   9.5 

11.5  fo  13.5 

Brass  on  Brass 

40  to       50 

20,000  to  25,000 
5.000  to    6,700 

6  to    8 

12.5  to  16.5 

Screwed  Contact 

Copper  to  Copper 

150  to     200 

23  to  31 

3    to   4.5 

Composition  to  Copper 

125  to     150 

6,700  to    8,000 

19  to  23     4.5  to    5.5 

Composition  to  Composition 

100  to     125 

8,000  to  10,000 

15  to  20 

5    to   6.5 

Clamped  Contact 

Copper  to  Copper 

100  to     125 

8,000  to  10,000 
10,000  to  13,000 

15  to  20 

5    to    6.5 

Composition  to  Copper 

75  to     100 

12  to  16 

6    to    8.5 

Composition  to  Composition 

70  to       90 

11,000  to  14,000 

11  to  14 

7    to     9 

Fitted  Contact 
(Taper  Plugs) 

Copper  to  Copper 

125  to      175 

5,700  to    8,000 

20  to  28 

3.5  to     5 
5    to     7 

Composition  to  Copper 

100  to      125 

8,000  to  10,000 

15  to  20 

Composition  to  Composition 

75  to     100 

10,000  to  13,000 

12  to  16 

6    to    8.5 

Pitted  and 
Screwed  Contact 

Copper  to  Copper 

200  to     250 
175  to     200 

4,000  to    5,000 

30  to  40 

2.5  to   3.5 

Composition  to  Copper 

5,000  to    5,700 

28  to  31 

3    to   3.5 

Composition  to  Composition 

150  to      175 

5,700  to    6,700 

23  to  28 

3.5  to   4.5 

Cross-section 

Copper  Wire 

1,200  to  2,000 

500  to      800 

175  to  300 
150  to  250 

.35  to    .55 

Copper  Wire  Cable 

1,000  to  1,600 

600  to    1,000 

.4    to    .65 

Copper  Rod 

800  to  1,200 

800  to    1.200 

125  to  175 

.55  to    .80 

Composition  Casting 

500  to     700 

1,400  to    2,000|  75  to  110^  .90  to  1.35 

Brass  Casting 

300  to     400 

2,500  to    3,300   45  to    60 

1.60  to  2.25 

CHAPTER  X. 

MECHANICAL    CALCULATIONS    ABOUT    ARMATURE. 

51.    Armature  Shaft. 

The  length  of  the  armature  shaft,  varying  considerably  foi 
the  different  arrangements  of  the  field  magnet  frame,  depends 
upon  the  type  chosen,  and,  since  the  length  of  the  commutator 
depends  upon  the  current  output  of  the  machine,  even  varies 
in  dynamos  of  equal  capacity  and  of  same  design,  but  of  differ- 
ent voltage,  a  general  rule  for-  the  length  of  the  shaft  can 
therefore  not  be  given. 

Its  diameter,  however,  directly  depends  only  upon  the  out^ 
put  and  the  speed  of  the  dynamo,  and  can  be  expressed  as 
a  function  of  these  quantities,  different  functions,  however, 
being  employed  for  various  portions  of  its  length.  For,  while 


&//////A 


-Si  __  .*» 

"~"9    "  ,  ^^£,1.7.3"" 


y////////// 


Fig.  126. — Dimensions  of  Armature  Shaft. 

in  the  bearing  portions,  db,  Fig.  126,  torsional  strength  only 
has  to  be  taken  into  account,  the  center  portion,  dc,  between 
the  bearings,  which  carries  the  armature  core,  is  to  be  calcu- 
lated to  withstand  the  torsional  force  as  well  as  the  bending 
due  to  the  weight. 

For  steel  shafts  the  author  has  found  the  following  empirical 
formulae  to  give  good  results  in  practice : 

For  bearing  portions: 

4,  =  k,  x  V^  x  yffi,      (122) 

where  </b  =  diameter  of  armature  shaft,  at  bearings,  in  inches; 
P'  =  capacity  of  dynamo,  in  watts; 
N  =  speed,  in  revolutions  per  minute; 
£8    =  constant,  depending  upon  the  kind  of  armature, 
see  Table  XLIX. 


51] 


MECHANICAL   CALCULATIONS. 


185 


The  value  of  k%  varies  between  .0025  and  .005,  as  follows: 

TABLE  XLIX.— VALUE  OF  CONSTANT  IN  FORMULA  FOR  JOURNAL- 
DIAMETER  OF  ARMATURE  SHAFT. 


KIND  or  ARMATURE. 

VALUE  OP 

High  speed  drum  armature  

.0025 

.003 

.004 

.005 

For  core  portion  : 


<ZC  = 


X 


(123) 


where   dG    —  diameter  of  core  portion  of  armature  shaft,  in 

inches; 

P'    =  capacity  of  machine,  in  watts; 
N   —  speed,  in  revolutions  per  minute; 
k9    —  constant   depending   upon   output   of   machine, 

see  Table  L. 

This  constant  indicates  the  dependence  of  the  diameter  of 
the  shaft  upon  the  length  between  its  supports;  and  since  the 
weight  supported  and  also  the  length  supporting  it  increase 
with  the  output,  it  is  evident  that  k9  has  a  greater  value  the 
larger  the  output  of  the  machine.  For  capacities  up  to  2,000 
kilowatts,  k9  numerically  ranges  between  i  and  1.8,  thus: 

TABLE  L. — VALUE  OF  CONSTANT  IN  FORMULA  FOR  DIAMETER  OF  CORE 
PORTION  OF  ARMATURE  SHAFT. 


CAPACITY,  IN  WATTS. 
P' 

VALUE  OF 
&9. 

Up 

to        1,000  wa 
5,000 
'      10,000 
50,000 
100,000 
200,000 
500,000 
1,000,000 
2,000,000 

ttts  

1 
1.1 
1.2 
1.3 
1.4 
1.5 
1.6 
1.7 
1.8 

""  

1 86 


DYNAMO-ELECTRIC  MACHINES. 


[§51 


Considering  the  speeds  given  in  Tables  X.,  XI.,  and  XII. ,  § 
21,  for  various  outputs,  we  obtain  the  following  Tables  LI., 
LIT.,  and  LIU.,  giving,  respectively,  the  diameters  of  shafts 
for  drum  armatures,  for  high-speed  ring  armatures,  and  for  low- 
speed  ring  armatures: 

TABLE  LI. — DIAMETERS  OF  SHAFTS  FOR  DRUM  ARMATURES. 


SPEED, 

DIAMETER  OF  ARMATURE  SHAFT,  IN  INCHES. 

IN 

CAPACITY, 

IN 

KEVOLUTIONS 
PER  MINUTE 

Bearing  Portion. 

Core  Portion. 

WATTS. 

(FROM 

4  /  — 

P 

TABLE  X.) 

N. 

db  =  .0025  }/~F  X  V~N 

kg 

*  =  *  x  j/r 

100 

3,000 

V 

.9 

f 

250 

2,700 

6 

.95 

500 
1,000 

2,400 
2,200 

i 

1 
1 

it 

2,000 

2,000 

t 

1.05 

1 

3,000 

,900 

ft 

1.1 

li 

5,000 

,800 

H 

1.15 

H 

10,000 

,700 

If 

1.2 

2 

15,000 

,600 

H 

1.25 

2i 

20,000 

,500 

1.25 

H 

25,000 

,350 

2| 

1.25 

*t 

30,000 

,200 

2^- 

1.3 

3 

50,000 

,050 

3 

1.3 

31 

75,000 

900 

3f 

1.35 

2 

100,000 

750 

** 

1.4 

4f 

150,000 

600 

4f 

1.45 

54 

200,000 

500 

5* 

1.5 

6f 

300,000 

400 

6 

1.55 

8 

For  wrought  iron  shafts  the  diameters  obtained  by  formulae 
(122)  and  (123),  or  those  taken  from  Tables  LI.,  LIL,  and 
LIU.,  respectively,  are  to  be  multiplied  by  1.25,  that  is,  in- 
creased by  25  per  cent. 

52.  Driving  Spokes. 

Ring  armature  cores  usually  are  attached  to  the  shaft  either 
by  means  of  spider  frames  or  of  skeleton  pulleys.  In  both 
cases  the  driving  of  the  conductors  is  effected  by  a  number  of 
spokes,  which  respectively  form  part  of  the  spider  itself,  Fig. 
12.7,  or  of  a  separate  driving  frame  keyed  to  the  skeleton  pulley, 
Fig.  128,  page  188. 


§51]  MECHANICAL    CALCULATIONS.  187 

TABLE  LII. — DIAMETERS  OF  SHAFTS  FOR  HIGH-SPEED  RING  ARMATURES. 


SPEED, 

DIAMETER  OP  ARMATURE  SHAFT,  IN  INCHES.  ~~ 

IN 

CAPACITY, 

IN 

REVOLUTIONS 
PER  MINUTE 

Bearing  Portion. 

Core  Portion. 

WATTS. 

(PROM 

A            y—  . 

TABLE  XI.) 

4  

_ 

/  f 

F 

jr. 

db  =  .003  4/^P  X  V  M 

9 

c=  9X  y  F- 

100 

2,600 

* 

.9 

i 

250 

2,400 

f 

.95 

500 

2,200 

1 

yi 

1,000 

2,000 

1 

1 

£ 

2,500 

1,700 

1 

1.05 

li 

5,000 

1,500 

If 

1.1 

10,000 

1,250 

If 

1.2 

2 

25,000 

1,000 

2! 

1.25 

a*  ' 

50,000 

800 

1.3 

3f 

100,000 

600 

4f 

1.4 

5 

200,000 

500 

6* 

1.5 

6f 

300,000 

450 

.55 

400,000 

400 

8* 

.55 

9 

600,000 

350 

10 

.6 

10* 

800,000 

300 

11 

.65 

12 

1,000,000 

250 

12 

.7 

18* 

1,500,000 

225 

14 

1.75 

15f 

2,000,000 

200 

16 

1.8 

18 

TABLE  LIII. — DIAMETERS  OF  SHAFTS  FOR  LOW-SPEED  RING  ARMATURES. 


CAPACITY, 

IN 

WATTS. 

SPEED, 

IN 

REVOLUTIONS 
PER  MINUTE 

(PROM 

DIAMETER  op  ARMATURE  SHAPT,  IN  INCHES. 

Bearing  Portion. 

Core  Portion. 

A     /  

TABLE  XII.) 

4 

/    f 

P 

jr. 

db  =  .005  i/P'X  Y^T 

9 

c=     9X    ]/  N 

2,500 

400 

li 

.05 

If 

5,000 

350 

1* 

.1 

10,000 

300 

2 

.2 

a§ 

25,000 

250 

$1 

.25 

4 

50,000 

200 

4* 

.3 

5^ 

100,000 

175 

5f 

.4 

Ql 

200,000 

150 

.5 

9 

300,000 

125 

9* 

.55 

lOf 

400,000 

100 

10 

.55 

12i 

600,000 

90 

12 

.6 

14i 

800,000 

80 

13i 

.65 

16* 

1,000,000 

75 

15 

.7 

18i 

1,500,000 

70 

18 

.75 

22 

2,000,000 

65 

20 

1.8 

24* 

1 88 


D  YNA MO-ELECTRIC  MA  CHINES. 


[§52 


In  dimensioning  these  driving  spokes,  on  the  one  hand  suf- 
ficient mechanical  strength  for  driving  should  be  provided, 
while  on  the  other  hand,  if  spiral  winding  is  to  be  used,  not 


Fig.    127. — Ring  Armature  Driven  by  Spiders. 

more  than  necessary  of  the  inner  winding  circumference  should 
be  made  unavailable. 

For  the  latter  reason  the  axial  breadth  of  the  spokes,  ^s, 
Figs.  127  and  128,  is  to  be  made  as  large  as  the  construction 
of  the  armature  allows,  and  their  thickness,  h^  calculated  to 
give  the  requisite  strength. 

Multiplying  equation  (95)  for  the  circumferential  force  per 


Fig.  128. — Ring  Armature  Driven  by  Pulley  and  End  Rings. 

armature  conductor  (§  41)  by  the  number  of  effective  conduc 
tors,  we  obtain  the  total  peripheral  force  of  the  armature: 


a   =  /.    X    ^e    X    ft\   =    -7375     X 


....(124) 


§52]  MECHANICAL   CALCULATIONS.  189 

and,  allowing  a  factor  of  safety  of  about  4,  we  get: 

Dividing  P'&  by  the  total  number  of  spokes,  we  have  the 
pull  for  each  spoke,  and  this  multiplied  by  the  leverage  gives 
the  external  momentum  acting  on  each;  the  latter  must  be 
equal  to  the  internal  momentum,  /.  <?.,  the  product  of  the 
modulus  of  the  cross-section  and  the  safe  working  stress  of 
the  material.  In  consequence,  we  have  the  equation: 

P' 

3  X  - 


s  X 

—^~     </s-  6 

or 


(125) 


in  which  £s  =  smallest  width  of  spoke  (parallel  to  shaft),   in 

inches; 
tis  =  smallest  thickness  of  spoke   (perpendicular  to 

shaft),  in  inches; 

/s  =  leverage  at  smallest  spoke  section,  /.  <?.,  distance 
of  smallest  section  from  active  armature  con- 
ductors, in  inches; 

«s  =  total  number  of  spokes  per  armature; 
P'  =  total  capacity  of  dynamo,  in  watts; 
vc  =  conductor   velocity   of  armature,    in   feet    per 

second; 
/s  =  safe  working  load  of  material,   in  pounds  per 

square  inch; 
for  cast  iron  .......  -A  =    5>°°°  lbs-  Per  square  inch. 

11   brass  ...........      =    6,000  "  " 

4<   phosphor-bronze       =    7,000  il  " 

"   wrought  iron.  ...       =  10,000  " 

"   aluminum  bronze      =  12,000  "  " 

"   cast  steel  .......      =15,000  *'  " 

For  spiral  windings,  now,  £s,  as  stated  above,  is  given  by 
making  it  as  large  as  possible,  and  from  (125)  we  therefore 
obtain:  « 


I90 


DYNAMO-ELECTRIC  MACHINES. 


[§53 


For  windings  external  to  the  core,  h*  may  be  fixed  and  then 
calculated  from: 

4 


>8  =  l8x^rx^,x>i%x 


(127) 


For  very  heavy  duty  dynamos  a  larger  factor  of  safety 
should  be  taken,  say  from  6  to  8;  this  will  change  the  numeri- 
cal coefficient  of  formulae  (125)  and  (127)  into  27  to  36,  and 
that  of  equation  (126)  into  5.3  to  6,  respectively. 

53.  Armature  Bearings. 

To  determine  the  size  of  the  armature  bearings,  ordinary 
engineering  practice  ought  to  be  followed.  In  machine 
design,  on  account  of  the  increased  heat  generation  at  higher 
velocities,  it  is  the  rule  to  provide  a  larger  bearing  surface  the 
higher  the  speed  of  the  revolving  shaft.  This  rule  may,  for 
dynamo  shafts,  be  expressed  by  the  formula: 


(128) 


where  /b  =  length  of  bearing,  in  inches; 

</b  =  diameter  of  bearing,  in  inches,  from  formula  (122); 

N=  speed  of  shaft  in  revolutions  per  minute; 

£10  =  constant  depending  upon  kind  of  armature  and  on 

capacity  of  dynamo.     (See  Table  LIV.) 
The  numerical  values  of  £10  range  between  .1  and  .225  for 
high-speed  armatures,  and  from  .15  to  .3  for  low-speed  arma- 
tures, as  follows: 

TABLE  LIV.  —  VALUE  OF  CONSTANT  IN  FOBMULA  FOR  LENGTH  OF 
ARMATURE  BEARINGS. 


CAPACITY, 


VALUE  OF  CONSTANT 


IN 

KILOWATTS. 

High-Speed 
Armatures. 

Low-Speed 
Armatures. 

Up  to          5 

.1 

.15 

10 

.1 

.175 

50 

.125 

.2 

100 

.15 

.225 

500 

.175 

.25 

1,000 

.2 

.275 

2,000 

.225 

.3 

§53] 


MECHANICAL    CALCULA  TIONS. 


191 


Applying  these  values  to  formula  (128),  and  using  the  jour- 
nal diameters  previously  determined,  the  following  Tables 
LV.,  LVL,  and  LVII.  are  obtained,  giving  the  sizes  of  bearings 
for  drum  armatures,  high-speed  ring  armatures,  and  low-speed 
ring  armatures,  respectively: 

TABLE  LV.— BEARINGS  FOR  DRUM  ARMATURES. 


SIZE  OF  BEARING. 

SPEED 

CAPACITY, 

VALUE 

IN  REVS. 

IN 

KILO- 
WATTS. 

OF 

CONSTANT 
&o. 

PER  MIN. 

(PROM 

TABLE  X.) 

N. 

Diameter 
(from 
Table  LI.) 
j 

Length. 
*b  =  *M  X  db  X     ^' 

Ratio, 
'b^b 

db 
b 

.1 

3,000 

A 

1 

5.3 

.25 

_ 

2,700 

ft 

If 

5.2 

.5 

, 

2,400 

? 

2i 

4.9 

1 

2,200 

T9* 

2f 

4.7 

2 

2,000 

3f 

4.5 

3 

1,900 

If 

4 

4.3 

5 

1,800 

if 

4f 

4.2 

10 

.1 

1,700 

if 

6| 

4.2 

15 

.105 

1,600 

i* 

7| 

4.2 

20 

.11 

1,500 

2i 

9 

4.2 

25 

.115 

1,350 

2f 

10 

4.2 

30 

.12 

1,200 

21 

10i 

4.2 

50 

.125 

1,050 

3 

12 

4.0 

75 

.13 

900 

3i 

14 

3.9 

100 

.14 

750 

4i 

15f 

3.8 

150 

.15 

600 

4f 

17i 

3.7 

200 

.16 

500 

5i 

18f 

3.6 

300 

.175 

400 

6 

21 

3.5 

54.  Pulley  and  Belt. 

The  pulley  diameter  is  determined   by  the   speed   of  the 
dynamo  and  the  linear  belt  velocity: 


_ 
~ 


12  X  v* 
n   x  N 


_  , 

~  3'7 


where  Z>p  =  diameter  of  pulley,  in  inches; 

r'B  =  belt  speed,  in  feet  per  minute,  see  Table  LVIII. ; 
JV  =  speed  of  dynamo,  in  revolutions  per  minute. 
The  belt  speed  in  modern  dynamos  ranges  between  2,000 


I92  DYNAMO-ELECTRIC  MACHINES.  [§53 

TABLE  LVI.— BEARINGS  FOR  HIGH-SPEED  RING  ARMATURES. 


SIZE  OF  BEARING. 

SPEED 

CAPACITY, 

IN 

KILO- 

VALUE 

OP 

CONSTANT 

IN  REVS. 
PER  Mm. 

(FROM 

Diameter 

Length. 

Ratio. 

WATTS. 

£10. 

TABLE  XI.) 

N. 

(from 
Table  LII.) 

<*b 

ib  =  &10  x  db  x  VN. 

«b  :<*b 

.1 

.1 

2,600 

i 

li 

5.0 

.25 

.1 

2,400 

11 

5.0 

.5 

.1 

2,200 

J 

si 

4.75 

1 

.1 

2,000 

I 

2f 

4.4 

2.5 

.1 

1,700 

4i 

4.1 

5 

.1 

1,500 

If 

5f 

3.9 

10 

.11 

1,250 

If 

6f 

3.85 

25 

.12 

1,000 

2f 

10 

3.8 

50 

.13 

800 

3i 

13 

3.7 

100 

.15 

600 

4f 

17i 

3.7 

200 

.16 

500 

6f 

23 

3.6 

300 

.17 

450 

7i 

27 

3.6 

400 

.175 

400 

8i 

30 

8.5 

600 

.18 

350 

10 

33i 

3.35 

800 

.19 

300 

11 

36 

3.3 

1,000 

.2 

250 

12 

38 

3.2 

1,500 

.21 

225 

14 

45 

3.2 

2,000 

.225 

200 

16 

51 

3.2 

TABLE  LVIL—  BEARINGS  FOR  LOW-SPEED  RING  ARMATURES. 


SIZE  OP  BEARING. 

SPEED 

CAPACITY, 

VALUE 

IN  REVS. 

IN 

KILO- 
WATTS. 

OP 

CONSTANT 

&10. 

PER  MIN. 
(FROM 
TABLE  XII.) 

N. 

Di«meter 
(from 
Table  LIII.) 

<*b 

Length. 

ib  =  &io  x  db  x  VN. 

Ratio. 
*b   :^b 

2.5 

.15 

400 

H 

3f 

3.0 

5 

.16 

350 

H 

4i 

3.0 

10 

.17 

300 

2 

51 

2.9 

25 

.18 

250 

3i 

8f 

28 

50 

.19 

200 

4i 

IH 

2.7 

100 

.20 

175 

H 

15i 

265 

200 

.21 

150 

7f 

20 

2.6 

300 

.23 

125 

9i 

23f 

2.6 

400 

.25 

100 

10 

25 

2.5 

600 

.265 

90 

12 

30 

2.5 

800 

.27 

80 

13i 

32i 

2.4 

1,000 

.28 

75 

15 

36^ 

2.4 

1,500 

.29 

70 

18 

43i 

2.4 

2,000 

.30 

65 

20 

48 

2.4 

54] 


MECHANICAL   CALCULATIONS. 


and  6,000  feet  per  minute  (=  600  and  1,800  metres  per  minute), 
as  follows: 

TABLE  LVIII. — BELT  VELOCITIES  FOB  HIGH-SPEED  DYNAMOS  OP 
VARIOUS  CAPACITIES. 


BELT  SPEED,  #B 

CAPACITY 

Feet  per  Minute. 

Metres  per  Minute. 

Up 
2.5 

to     5 

"    25 

2,000 
3,000 

to  3,000 
"   4,000 

600  to      900 
900  "  1,200 

10 

"  100 

4,000 

"   5,000 

1,200  "  1,500 

50 

"  500 

5,000 

11   6,000               1,500  "  1,800 

The  pull  at  the  pulley  circumference,  in  pounds,  is: 

p   -  33>QQQ    X  HP   =  33,ooo  X  HP 
'  ~ 


12 


Watts 


For  an  arc  of  belt  contact  of  180°,  which  can  safely  be  as- 
sumed for  dynamo  pulleys,  the  pull  Fv,  is  to  be  multiplied  by 
1.4  in  order  to  obtain  the  tension  on  the  tight  side  of  the  belt; 
hence  the  greatest  strain  upon  the  belt: 


=  1.4  x 


p; 

=  62  X   - 
z/» 


Allowing  300  pounds  per  square  inch  as  the  safe  working 
strain  of  leather,  the  necessary  sectional  area  of  the  belt  can 
be  found  from 

--  •'  X   -£-;     .(130) 


£B    =  width  of  belt,  in  inches; 

/£„    =  thickness  of  belt,  in  inches; 

FB  =  greatest  strain  in  belt,  /.  <?.,  tension  on  its  tight  side,  in 

pounds; 

P'   —  capacity  of  dynamo,  in  watts; 
i\    —  belt  speed,  in  feet  per  minute,  Table  LVIII. 


1 94 


D  YNA  MO-ELECTRIC  MA  CHINES. 


54 


The  approximate  thicknesses  for  the  various  kinds  of  belts 
are: 

Single  belt AB  —  T3^-  inch 

Light  double  belt "  =  A    " 

Heavy  double  belt "  =  H    " 

Three-ply  belt 


Inserting  these  figures  into  (130),  the  width  of  the  belt  is 
obtained: 


Single  belt 


?          P'  P' 

=  4  x--  =  i.i  x-      (131) 

T6  ^B  ^B 


Light  double  belt. . .  A  =  ^-  x  —  =  .7  X  —     (132) 

-fis  Vv  V-* 


TABLE  LIX. — SIZES  OF  BELTS  FOR  DYNAMOS. 


WIDTH  OF  BELT,  IN  INCHES. 

OUTPUT 

OF 

DYNAMO 

IN 

THICKNESS 

OF 

BELT, 

Belt  Speed,  in  Feet  per  Minute  : 

KILO- 

INCH. 

i 

I 

( 

WATTS. 

. 

2,000 

2,500 

3,000 

3,500 

4,000 

4,500 

5,000 

5,500 

6,000 

1 

r  s 

.8 

.7 

.6 

2 

? 

1.6 

1.3 

1.1 

3 

2.3 

1.8 

1.5 

1.3 

1.2 

" 

5 

3.1 

3.0 

2.5 

2.1 

1.9 

.  . 

.  . 

.  . 

. 

7.5 

5.4 

4.4 

3.6 

3.1 

2.7 

10 

^  ft 

7.1 

5.6 

4.7 

4.0 

3.5 

s!i 

2!s 

. 

15 
20 

"fab  T^ 

10.3 
13.4 

8.3 
10.7 

6.9 
9.0 

5.9 

7.7 

5.2 
6.7 

4.6 
6.0 

4.1 
5.4 

•• 

25 

10.9 

9.4 

8.2 

7.3 

6.6 

, 

30 

02    A 

13 

11.1 

9.7 

8.6 

7.8 

.  . 

. 

40 

A 

17 

14.6 

12.8 

11.4 

10.2 

50 

A 

21 

18.0 

15.8 

14 

12.7 

ii!s 

l6!  5 

60 

.  . 

25 

21.4 

18.8 

16.7 

15 

13.7 

12.5 

75 

3 

31 

26.5 

23.2 

20 

18.5 

17 

15.5 

100 

I    ft 

•  • 

30 

27 

24.4 

22.2 

20.4 

150 

03       ~&7£ 

29 

25.7 

23 

21 

19.3 

200 

. 

'.'.      33 

29.2 

26.3 

24 

22 

250 

OC§  FJ 

.  . 

..     140.7 

36.2 

32.6 

29.6 

27.2 

300 

Q         11 

•• 

51.3 

45.5 

41 

37.3 

34.2 

400 

t    t>>  7 

I 

48.5 

43 

38.7 

35.2 

32.2 

500 

CO  i-^^y 

•• 

60 

53.5 

48 

44 

40 

§54]  MECHANICAL    CALCULATIONS.  *S 

Heavy  double  belt. .  A  =    \\  x  ^  =   .6  X  ^     (133) 


Three-ply  belt 

Single  belts  are  used  for  all  the  smaller  sizes,  up  to  100  KW 
output,  light  double  belts  up  to  200  KW,  heavy  doubles  up  to  400 
KW,  and  three-ply  belts  for  capacities  from  400  KW  up. 

Based  upon  the  above  formulae  the  author  has  prepared  the 
preceding  Table  LIX.,  from  which  the  belt  dimensions  for  vari- 
ous outputs  and  for  different  belt  speeds  can  readily  be  taken. 

The  width  of  the  belt  being  thus  determined,  the  breadth  of 
the  pulley-rim  is  found  by  adding  from  ^  inch  to  2  inches, 
according  to  the  width  of  the  belt. 


PART  III. 


CALCULATION  OF  MAGNETIC  FLUX. 


CHAPTER  XL 

USEFUL    AND    TOTAL    MAGNETIC    FLUX. 

55.  Magnetic  Field.    Lines  of  Magnetic  Force.    Magnetic 
Flux.    Field-Density. 

The  surrounding  of  a  magnetic  body,  as  far  as  the  magnetic 
effects  of  the  latter  extend,  is  called  its  Magnetic  Field. 

According  to  the  modern  theory  of  magnetism,  magnetic 
attractions  and  repulsions  are  assumed  to  take  place  along 
certain  lines,  called  Lines  of  Magnetic  Force;  the  magnetic 
field  of  a  magnet,  therefore,  is  the  region  traversed  by  the 
magnetic  lines  of  force  emanating  from  its  poles. 

The  lines  of  magnetic  force  are  assumed  to  pass  out  from 
the  north  pole  and  back  again  into  the  magnet  at  its  south 
pole;  \\\€\*  direction,  therefore,  indicates  tint  polarity  of  the  mag- 
netic field. 

The  total  number  of  lines  of  magnetic  force  in  any  magnetic 
field  is  termed  its  Magnetic  Flow,  or  Magnetic  Flux,  and  is  a 
measure  of  the  amount,  or  quantity  of  its  magnetism. 

The  density  of  the  magnetism  at  any  point  within  the  region 
of  magnetic  influence  of  a  magnet,  or  the  Field  Density  of  a 
magnet,  is  expressed  by  the  number  of  these  magnetic  lines  of 
force  per  unit  of  field  area  at  that  point,  measured  perpendicu- 
larly to  their  direction. 

The  Unit  of  Field  Density — that  is,  the  field  density  of  a 
unit  pole — is  i  line  of  magnetic  force  per  square  centimetre  of 
field  area,  and  is  called  i  gattss. 

A  Single  Line  of  Force,  or  the  Unit  of  Magnetic  Flux,  is  that 
amount  of  magnetism  that  passes  through  every  square  centi- 
metre of  cross-section  of  a  magnetic  field  whose  density  is 
unity.  To  this  unit  the  name  of  i  weber  has  been  given. 

A  Magnet  Pole  of  Unit  Strength  is  that  which  exerts  unit 
force  upon  a  second  unit  pole,  placed  at  unit  distance  from  the 
former.  The  lines  of  force  of  a  single  pole,  concentrated  in 
one  point,  are  straight  lines  emanating  from  this  point  to  all 


200  DYNAMO-ELECTRIC  MACHINES.  [§56 

directions;  /.  e.,  radii  of  a  sphere.  The  surface  of  a  sphere  of 
i  centimetre  radius  is  4  n  square  centimetres;  a  pole  of  unit 
strength,  therefore,  has  a  magnetic  flux  of  4  it  absolute  or 
C.  G.  S.  lines  of  magnetic  force,  or  of  4  TC  webers. 

The  number  of  C.  G.  S.  lines  of  force,  or  the  number  of 
webers  expressing  the  strength  of  a  certain  magnetic  field, 
must  consequently  be  divided  by  4  TT,  or  by  12.5664,  in  order  to 
give  that  same  field  strength  in  absolute  units  of  magnetism, 
*".  £.,  in  unit-poles. 

A  magnetic  field  of  unit  intensity  also  exists  at  the  center  of 
curvature  of  an  arc  of  a  circle  whose  radius  is  i  centimetre 
and  whose  length  is  i  centimetre,  when  a  current  of  i 
absolute  electromagnetic  unft  of  intensity,  or  of  10  practical 
electromagnetic  units,  that  is,  of  10  amperes,  flows  through 
this  arc.  Therefore,  the  unit  of  magnetic  flux,  i.  <?.,  i 
C.  G.  S.  line  of  force,  or  i  weber,  is  equal  to 

10 
4  n 

practical  electromagnetic  units,  or  one  practical  electromag- 
netic unit 

4  n 
—         -  webers. 


56.    Useful  Flux  of  Dynamo. 

The  total  number  of  lines  of  force  cutting  the  armature  con 
ductors  is^called  the  Useful  Flux  of  the  dynamo. 
According  to  the  definition  given  in  §  15,  we  have: 

^    .  Number  of  C.  G.  S.   Lines  cut  per  second 

8  —  • 


Let  now  $  —  total  number  of  useful  lines,  or  useful  flux,  in 

webers; 
NQ  =  number  of  conductors  all   around   pole-facing 

circumference  of  armature; 
Ny.  =  nc  X  n&  ,  for  ring  armatures  ; 
JVC  =  2  x  nc  X  «a»  lor  drum  armatures  and  for  drum- 
wound  ring  armatures  ; 


§56]  USEFUL  AND    TOTAL  MAGNETIC  FLUX.  201 

(where  nc  =  number  of  commutator-divisions, 

n&  =  number   of   turns    per    commutator- 
division, 
nc  x  #a  =  total  number  of  convolutions  of 

armature,  see  §  25); 

JV  =  speed,  in  revolutions  per  minute;  and 
n'p  =  number  of  bifurcations  of  current  in  armature, 
/".   <?.,  number  of  pairs  of  armature  portions 
connected  in  parallel,  see  §  45 ; 
then, — 

i  conductor  in  i  revolution  cuts  2  <&  lines  of  force •, 

for,  the  $  lines  emanating  from  all  the  north  poles,  after  pass- 
ing the  armature  core,  return  to  the  south  poles,  hence  pass 
twice  across  the  air-gaps,  and,  in  consequence,  are  cut  twice  in 
each  revolution  by  every  armature  conductor. 
The  armature  makes 

K 

60 

revolutions  in  i  second,  hence, 

JV 

i  conductor  in  i  second  cuts  2  <&  x  ~r~  lines. 

oo 

Each  one  of  the  2  n'p  parallel  armature  portions   contains 


_      „' 

2  n  p 

conductors  connected  in  series;  in  each  of  these  2  ;z'p  arma- 
ture circuits,  therefore, 

N  N         N, 
5-  conductors  in  i  second  cut  2  $  X    -r-  X 


60  ~  2  »'p 


But,  according  to  the  law  of  the  divided  circuit,  the  E.  M.  F. 
generated  in  one  of  the  parallel  branches  is  the  output  voltage 
of  the  machine;  the  E.  M.  F.  generated  by  any  armature,  con- 
sequently, by  virtue  of  (135),  is 


and  from  this  we  obtain  the  number  of  useful  lines  required  to 
produce  the  E.  M.  F.  of  E'  volts,  thus  : 

_  6  X  <  X  E  X  io9. 


202  DYNAMO-ELECTRIC  MACHINES.  [§57 

For  dynamos  with  but  one  pair  of  parallel  circuits  in  the 
armature,  i.  <?.,  for  bipolar  machines  and  for  multipolar  dynamos 
with  series  connections,  we  have  ;/'p  =.  i,  see  (112)  and  (113), 
and  the  useful  flux  for  this  special  case  is: 

6X£'X    IO'B 
Nc  x&~ 

This  formula  also  gives  the  useful  flux  per  pole  in  multipolar 
dynamos,  with  parallel  grouping,  and  therefore  in  text-books 
is  usually  given  instead  of  (137)  as  the  general  formula  for  the 
useful  flux  of  a  dynamo,  which,  however,  is  not  strictly  correct, 
and,  in  consequence,  misleading. 

57.  Actual  Field  Density  of  Dynamo. 

According  to  the  definition  given  in  §  55,  the  actual  field 
density  of  a  dynamo  is  the  total  useful  flux  cutting  the  armature 
conductors,  divided  by  the  area  of  the  actual  magnetic  field, 
thus: 

3e*  =  -f-»     (139) 

of 

where  3C"  =  field  density,  in  lines  of  force  per  square  inch; 

$  =  useful  flux,  in  webers,  from  formula  (137)  or  (138), 
respectively;  and 

St  —  actual  field-area,  in  square  inches,  /.  *.,  area  occu- 
pied by  the  effective  armature  conductors. 

The  same  formula  also  holds  good  for  the  metric  system, 
the  density,  3C,  in  gausses,  being  obtained,  if  the  area,  Sf ,  is 
expressed  in  square  centimetres. 

The  actual  field  density,  calculated  from  (139),  is,  in  general, 
slightly  different  from  the  original  field  density,  selected  from 
Table  VI.,  §  18,  and  used  for  the  determination  of  the  length 
of  armature  conductor,  for  the  reason  that,  in  practice,  the 
length  of  the  polar  arc  is  not  fixed  with  relation  to  exactly  ob- 
taining the  assumed  field  density,  but  is  dimensioned  according 
to-a  construction  rule  having  reference  to  the  ratio  of  the 
distance  between  pole-corners  to  the  length  of  gap-spaces 
(see  §58). 

It  would  be  an  easy  matter  to  obtain  the  length  of  the  polar 
arc  and  the  percentage  of  its  embrace  from  the  assumed  field 


§  57]  USEFUL  AND    TOTAL  MAGNETIC  FLUX.  203 

density,  for,  supposing  that,  in  a  machine  with  smooth  arma- 
ture, the  length  of  the  polepieces  is  equal  to  that  of  the  arma- 
ture core,  we  would  simply  have  to  make  the  sum  of—  the 
lengths  of  the  polar  arcs  of  half  the  number  of  poles  equal  to 


or  the  percentage  of  the  polar  arc 


(UO) 


,      -         —  -  -, 

3C*.  X  4  X  dt  X  - 

in  which  ftl  =  percentage  of  polar  arc,  or  quotient  of  sum  of 
all  polar  arcs  by  circumference  of  mean  field- 
circle; 

$  —  useful  flux,  in  webers,  from  (137)  or  (138); 

3C"  =  assumed  field  density,  in  lines  per  square  inch, 
from  Table  VI.,  §  18; 

/a  =  length  of  armature  core,  in  inches,  formula  (40); 
and 

dt  =  mean  diameter  of  magnetic  field,  in  inches, 
which  is  given  by  the  core  diameter  of  the 
armature,  by  the  height  of  its  winding  space, 
and  by  the  clearance  between  the  armature 
winding  and  the  polepieces:  dt  —  d&  -|-  h&  -\-  hc  ; 
see  §  58. 

But  since  the  polar  embrace  so  determined  may  not  be  within 
the  limits  of  practical  design  in  accordance  with  the  construc- 
tion rule  referred  to,  it  is  advisable  not  to  follow  the  process 
indicated  by  formula  (140),  but  to  fix  the  distance  between  the 
pole-corners,  and  thereby  the  percentage  ftl  ,  by  that  rule,  and 
to  calculate  the  actual  field  density  corresponding  to  the  same 
by  formula  (142)  or  (146),  respectively. 

This  latter  method  is  in  no  way  objectionable,  as  the  new, 
actual  value  of  3C"  only  enters  the  calculation  of  the  magneto- 
motive force,  and  the  change  does  not  affect  any  of  the  previ- 
ous calculations  concerning  the  dimensions  and  the  winding 
data  of  the  armature.  For,  according  to  formula  (136),  the 
same  E.  M.  F.  will  be  generated  by  a  certain  number  of  con- 
ductors mpving  at  a  constant  speed,  as  long  as  the  total  useful 


204  DYNAMO-ELECTRIC  MACHINES.  [§57 

flux  remains  the  same;  the  E.  M.  F.  generated  by  a  certain 
armature,  therefore,  remains  constant  as  long  as  the  product 
field  density  and  field  area  is  kept  at  the  same  value,  and  it 
matters  not  whether  this  product  is  made  up  of  the  original 
field  density  and  an  area  corresponding  to  the  polar  embrace 
found  from  formula  (140),  or  of  a  larger  actual  density  and  a 


Fig.   129. — Field  Area  of  Bipolar  Dynamo. 

corresponding  reduced   field   area,    or   of   a   smaller   density 
spread  over  a  larger  area. 

a.   Smooth  Armatures. 

In  smooth-core,  armatures,  Fig.  129,  the  area,  St,  occupied  by 
the  effective  conductors,  is  obtained  from: 

S(  =  4  x  n~  X  fl\  X  lt  ;      (141) 

the  actual  field  density,  therefore,  by  inserting  (141)  into  (139) 
can  be  found: 

x"  =  -        -—        -,     (142) 

4  x  -2  x  ft\  x  /f 

where  JC''  =  actual  field  density  of  dynamo,   in  lines  of  force 

per  square  inch; 

0    =  total  useful  flux  of  machine,  in  webers,  from  for- 
mula (137)  or  (138); 
dt    =  mean  diameter  of  magnetic  field,  in  inches; 

=  \  K  +  4) ; 

d&  =  diameter  of  armature  core,  in  inches; 


§57]  USEFUL  AND    TOTAL  MAGNETIC  FLUX.  205 

</p  =  diameter  of  bore  of  polepieces,  in  inches; 

/3\  =  ratio  of  effective  field  circumference,  obtained 
from  the  percentage  of  polar  embracer  fi+  by 
means  of  Table  XXXVIIL,  §  38; 

/f   =  mean  length  of  magnetic  field,  in  inches, 


/a  =  length  of  armature  core,  in  inches; 
/p  =  length  of  polepiece,  in  inches; 

If  dt  and  /f  are  expressed  in  centimetres,  the  field  density  in 
gausses,  3C,  is  obtained  from  the  same  formula  (142). 

b.    Toothed  and  Perforated  Armatures. 

For  toothed  and  perforated  armatures,  the  area  St  occupied 
in  the  magnetic  field  by  the  effective  armature  conductors, 
cannot  be  directly  calculated  from  the  dimensions  of  the  arm- 
ature core,  since  the  path  area  of  the  actually  useful  flux  cut- 
ting the  conductors  depends  upon  too  many  conditions  to 
be  formulated  satisfactorily,  and  it  is,  therefore,  advisable  to 
compute  the  actual  field  density,  3C",  directly  from  the  electrical 
data  of  the  armature. 

According  to  §  15,  the  E.  M.  F.  generated  per  foot  of  effec- 
tive armature  wire  moving  at  a  velocity  of  i  foot  per  second 
in  a  field  of  the  density  of  i  line  per  square  inch,  is 

T^io- 


if  there  are  «'p  bifurcations  of  the  current  in  the  armature. 

For  the  total  effective  length  of  Ze  feet  of  conductor  moving 
at  the  speed  of  vc  feet  per  second  in  a  field  of  density  3C", 
therefore,  the  E.  M.  F.  generated  is 

E'  =  72  x,  I0"8  x  A  x  *c  x  oe",   ...  .(143) 
«P 

from  which  follows  the  field  density: 

«'' 


72  x  A  x  vc 

In  this,  Ze  depends  upon  the  polar  embrace,  which,  in  turn, 
is  determined  by  the  ratio  of  the  distance  between  pole-cor-' 


206  DYNAMO-ELECTRIC  MACHINES.  [§57 

ners  to  the  length  of  the  air  spaces,  and  can  be  expressed  in 
terms  of  the  total  active  length  of  wire,  by 

A  =  A  x  A     .............  (145) 

Inserting  (145)  into  (144),  we  obtain  the  actual  field  density: 
^XE'X   TO* 

72  x  A  x  A  x  z>c 

where  3C"  =  actual  field  density  of  dynamo,  in  lines  of  force 

per  square  inch; 

n'p  =  number  of  bifurcations  of  current  in  armature; 
E'  =  total  E.  M.   F.   to  be  generated   in    armature,  in 

volts; 

ft^  =  percentage  of  polar  arc,  see  §  58; 
Za  =  length  of  active  armature  conductor,  in  feet,  for- 

mula (26)  or  (148); 

ve  =  conductor  speed,  in  feet  per  second. 
The  field  density  in  metric  units  is  obtained  from 


if  Za  is  expressed  in  metres  and  vc  in  metres  per  second. 

Since,  in  a  newly  designed  armature,  on  account  of  rounding 
off  the  number  of  conductors  to  a  readily  divisible  number 
and  the  length  of  the  armature  to  a  round  dimension,  the 
actual  length,  Za  ,  of  the  armature  conductor,  in  general,  is 
somewhat  different  from  that  found  by  formula  (26),  (as  a  rule, 
a  little  greater  a  value  is  taken),  it  is  preferable  to  deduce  the 
accurate  value  of  Za  from  the  data  of  the  finished  armature  : 


L^NC  x       =x     -,    ......  (148) 

12  »«  12 

where  Nc  —  total  number  of  conductors  on  armature; 
/a    =  length  of  armature  core,  in  inches; 
nw  —  number  of  wires  per  layer;  \ 

«,    =  number  of  layers  of  armature  wire;        >  see  §  23. 
«j    =  number  of  wires  stranded  in  parallel.     ) 

Formula  (146)  for  the  actual  field  density  of  toothed  and 
perforated  armatures,  can  also  be  used  for  smooth  cores,  and 
may  be  applied  to  check  the  result  obtained  from  (142). 


§58] 


USEFUL   AND    TOTAL   MAGNETIC  FLUX. 


207 


For  the  application  to  smooth  armatures,  however,  the  polar 
embrace,  ftl ,  in  formula  (146)  and  (147),  is  to  be  replaced  by 
the  corresponding  value  of  the  effective  field  circumference,-/^-, 
obtained  from  the  former  by  means  of  Table  XXXVIII.,  §  38. 

If  it  is  desired  to  know  the  real  field  area  in  toothed  and 
perforated  armatures,  an  expression  for  St  can  be  obtained  by 
combining  formulae  (139)  and  (146),  thus: 


72  X 


X 


X  vc  X 


ae 


'  Xio8 


..(U9) 


This  formula,  which  gives  the  mean  effective  area  actually 
traversed  by  the  useful  lines  cutting  the  armature  conductors, 
is  very  useful  for  the  investigation  of  the  magnetic  field  of 
toothed  and  perforated  armatures. 

58.  Percentage  of  Polar  Arc, 

The  ratio  of  polar  embrace,  to  which  frequent  reference  has 
been  had  in  §  57,  is  determined  by  the  distance  between  the 
pole-corners  and  by  the  bore  of  the  polepieces. 

a.  Distance  Between  Pole-corners. 

The  mean  distance  between  the  pole-corners,  /p,  Fig.  130, 
depends  upon  the  length  of  the  gap-space  between  the  arma- 


Fig.   130. — Distance  Between  Pole-corners,  and  Pole  Space  Angle. 

ture  core  and  the  pole  face,  and  is  determined  by  the  rule  of 
makingthat  distance  from  1.25  to  8  times  the  length  of  the  two 
gap-spaces,  according  to  the  kind  and  size  of  the  armature  and 
to  the  number  of  poles,  see  Table  LX. 

Denoting  this  ratio  of  the  distance  between  the  pole-corners 


208 


DYNAMO-ELECTRIC  MACHINES. 


[§58 


to  the  length  of  the  gaps  by  £n  ,  this  rule  can  be  expressed  by 
the  formula: 

'p~Ax  K-4J (150) 

where  /p  =  mean  distance  between  pole-corners; 

dv  =  diameter  of  polepieces; 

d&=  diameter  of  armature  core;  for  toothed  and  per- 
forated armatures,  d&  is  the  diameter  at  the  bot- 
tom of  the  slots. 

The  value  of  k^  for  various  cases  may  be  chosen  within  the 
following  limits: 

TABLE  LX. — RATIO  OF  DISTANCE  BETWEEN  POLE-CORNERS  TO  LENGTH 
OF  GAP-SPACES,  FOR  VARIOUS  KINDS  AND  SIZES  OF  ARMATURES. 


VALUE  OF  RATIO  ku. 

CAPACITY 

IN 

KILO- 

Smooth  Armature. 

Toothed  or 

WATTS. 

Bipolar. 

Multipolar. 

Perforated  Armature. 

Drum. 

Ring. 

Drum. 

Ring. 

Bipolar. 

Multipolar. 

.1 

1.5 

2.5 

1.5 

2.5 

1.25 

1.25 

.25 

1.75 

3 

1.75 

2.75 

1.5 

1.3 

.5 

2 

3.5 

2 

3 

1.75 

1.4 

1 

2.25 

4 

2.25 

3.25 

2 

1.5 

2.5 

2.5 

4.5 

2.75 

3.5 

2.25 

1.6 

5 

3 

5 

3 

3.75 

2.5 

1.7 

10 

3.5 

5.5 

3.25 

4 

2.75 

1.8 

25 

4 

6 

3.5 

4.25 

3 

1.9 

50 

4.5 

6.5 

3.75 

4.5 

3.25 

2 

100 

5 

7 

4 

4.75 

3.5 

2.1 

200 

5.5 

7.5 

4.25 

5 

3.75 

2.2 

300 

6 

8 

4.5 

5.25 

4 

2.3 

400 

.... 

.... 

4.75 

5.5 

.... 

2.4 

600 

.... 

5 

5.75 

.... 

2.5 

800 

.... 

6 

.... 

2.6 

1,000 

.... 

. 

6.5 

.... 

2.7 

1,200 

.... 

... 

7 

.... 

2.8 

1,500 

7.5 

.... 

2.9 

2,000 



... 

• 

8 

3 

Whenever  £n  can  be  made  larger  than  given  in  the  above 
table  without  reducing  the  percentage  of  the  polar  embrace 
below  its  practical  limit,  it  is  advisable  to  do  so,  and  in  fact  this 
ratio  in  some  modern  machines  has  values  as  high  as  £n  =  12. 


§58] 


USEFUL   AND    TOTAL   MAGNETIC  FLUX. 


209 


b.   Bore  of  Polepieces. 

The  diameter  of  the  polepieces,  or  the  bore  of  the  field,  dv , 
is  given  by  the  diameter  of  the  armature  core,  the  height_o_L 
the  armature  winding,  and  the  clearance  between  the  armature 
winding  and  the  polepieces: 


2  x 


(151) 


d&  =  diameter  of  armature  core,  in  inches; 

h&  =  height  of  winding  space,  including  insulations  and 

binding  wires,  in  inches; 
hc  =  radial  height  of  clearance  between  external  surface 

of  finished  armature   and  polepieces,  in  inches; 

see  Table  LXI. 

TABLE  LXI. — RADIAL  CLEARANCE  FOR  VARIOUS  KINDS  AND  SIZES  OF 

ARMATURES. 


RADIAL  CLEARANCE,  hc. 

Smooth  Armature. 

DIAMETER 

OF 

Disc  or  Ribbon  Core. 

Wire  Core. 

Toothed 

ARMATURE. 

t 

>r 

Perforated 

Wire  Wound. 

Armature. 

Copper 

Wire 

Copper 

Bars. 

Wound. 

Bars. 

Drum. 

Ring. 

inches. 

cm. 

inch. 

mm. 

inch. 

mm. 

inch. 

mm. 

inch. 

mm. 

inch. 

mm. 

inch. 

mm. 

2 

4 

5 

10 

t 

0  8 

| 

1.2 
1.6 

•- 

•• 

ft 

0.8 
0.8 

1.2 

A 

0.8 

.. 

.. 

8 
12 
18 

15 
30 
45 

f 

1.6 

2.4 
3.2 

i 

1.2 
1.6 
2.4 

i 

1.6 

2.0 

! 

2.4 
3.2 

4.0 

t 

1.6 
2.4 

i 

1.2 
1.2 
1.6 

24 

30 
40 
50 

60 

75 
100 
125 

? 

4.0 

4.8 

i 

3.2 

4.0 
4.8 
5.6 

A 

A 

A 

2.4 
3.2 
4.0 

4.8 

I 

4.8 
5.6 
6.4 

7.2 

I 

3.2 
4.0 

4.8 
5.6 

i 

2.0 
2.4 
3.2 
4.0 

75 

100 

200 
250 

i 

6.4 

7.2 

uV 

5.6 
6.4 

$ 

8.0 
9.6 

f 

A 

6.4 

8.0 

4.8 
5.6 

125 

300 

~rV 

8.0 

.9 

7.2 

i 

6.4 

150 

400 

9.6 

TS 

8.0 

ins" 

7.2 

200 

500 

A 

11.2 

1 

9.6 

.  ••  , 

8.0 

210  DYNAMO-ELECTRIC  MACHINES.  [§58 

The  radial  clearance,  which  is  to  be  taken  as  small  as  pos- 
sible, in  order  to  keep  the  air-gap  reluctance  at  a  minimum, 
ranges  between  1/32  and  7/16  inch,  according  to  the  kind  of  the 
armature  and  its  size.  The  preceding  Table  LXI.  may  serve 
as  a  guide  in  fixing  its  limits  for  any  particular  case. 

The  above  table  shows  that  with  toothed  and  perforated 
armatures  the  smallest  clearance  can  be  used,  a  fact  which  is 
explained  by  the  consideration  that  the  exteriors  of  these 
armatures  offer  a  solid  body,  and  may  be  turned  off  true  to  the 
field-bore.  For  a  similar  reason  wire-core  armatures  need  a 
larger  clearance  than  disc-core  armatures,  since  the  former 
cannot  be  tooled  in  the  lathe,  and  have  to  be  used  in  the  more 
or  less  oval  form  in  which  they  come  from  the  press.  Since 
copper  bars  can  be  put  upon  the  body  with  greater  precision 
than  wires,  a  somewhat  larger  clearance  is  to  be  allowed  in  the 
latter  case.  Finally,  a  drum  armature,  in  general,  has  a 
higher  winding  space  than  a  ring  armature  of  same  size;  the 
unevenness  in  winding  will,  consequently,  be  more  prominent 
in  the  former  case,  and  therefore  a  drum  armature  should  be 
provided  with  a  somewhat  larger  clearance  than  a  ring  of 
equal  diameter. 

The  figures  given  in  Table  LXI.  may  be  considered  as  aver- 
age values,  and,  in  specially  favorable  cases,  may  be  reduced, 
while  under  certain  unfavorable  conditions  an  increase  of  the 
clearance  may  be  desirable. 

c.   Polar  Embrace. 

The  dimensions  of  the  magnetic  field  having  thus  been 
determined,  half  the  pole-space  angle,  a,  Fig.  130,  can  be 
found  from  the  trigonometrical  equation: 

sina  =  -£; (152) 

TP 

p  =  pole  distance,  from  formula  (150); 
dv  =  diameter  of  polepieces,  from  formula  (151). 

The  ratio  of  polar  embrace,  or  the  percentage  of  polar  arc, 
then,  is: 

90-  -ax^ 


§59]  USEFUL  AND    TOTAL  MAGNETIC  FLUX.  211 

in  which  a  =  half  pole-space  angle,  from  (152); 

«p  =  number  of  pairs  of  magnet  poles. 
From  (153)  follows,  by  transposition: 

-  90X(.  - 


from  which  the  pole-space  angle,  a,  can  be  calculated  in  the 
case  that  the  ratio  of  embrace,  ftl  ,  of  the  polepieces  is  given. 

59.  Relative  Efficiency  of  Magnetic  Field. 

The  useful  flux  of  the  dynamo  being  found  from  formula 
(137),  the  number  of  lines  of  force  per  watt  of  output,  at  unit 
conductor-velocity,  will  be  a  measure  for  the  magnetic  quali- 
ties of  the  machine,  and  may  be  regarded  as  the  relative 
efficiency  of  the  magnetic  field. 

The  field  efficiency  for  any  dynamo  can  accordingly  be 
obtained  from  the  equation: 


x  r 


x  Vc  =    ^  x 


where  #',,  =  relative  efficiency  of  magnetic  field,  in  webers  per 

watt  of  output  at  a  conductor  velocity  of  i  foot 

per  second. 

$    =  useful  flux  of  dynamo,  from  formula  (137)  or  (  138)  ; 
E'   —  total  E.   M.  F.   to   be  generated   in    machine,   in 

volts; 
/'     =  total    current    to    be    generated    in    machine,    in 

amperes; 

P'    =  E'  X  /'  =  total  capacity  of  machine,  in  watts; 
vc     =  conductor  velocity,  in  feet  per  second. 

The  numerical  value  of  this  constant,  $'P  ,  varies  between 
4,000  and  40,000  lines  of  force  per  watt  at  i  foot  per  second, 
according  to  the  size  of  the  machine,  the  lower  figure  corre- 
sponding to  the  highest  field  efficiency;  and  for  outputs  from 
1/4  KW  to  2,000  KW,  for  bipolar  and  for  multipolar  fields, 
respectively,  ranges  as  per  the  following  Table  LXIL,  which  is 
averaged  from  a  great  number  of  modern  dynamos  of  all  types 
of  field-magnets: 


212  DYNAMO-ELECTRIC  MACHINES.  [§59 

TABLE  LXIL — FIELD  EFFICIENCY  FOR  VARIOUS  SIZES  OF  DYNAMOS. 


CAPACITY, 
IN  KILOWATTS. 

VALUE  OP  $  'f 
IN  WEBERS  PER  WATT,  AT  UNIT  CONDUCTOR  VELOCITY. 

Bipolar  Fields. 

Multipolar  Fields. 

Up        to             .25 
.25  to           1 
1      to          10 
10     to         50 
50     to       100 
100      to       500 
500     to    1,000 
1,000     to    2,000 

15,000  to  40,000 
10,000  to  20,000 
8,000  to  15,000 
7,000  to  12,000 
6,000  to  10,000 
5,000  to    7,500 

10,000  to  20,000 
8,000  to  15,000 
7,000  to  12,000 
6,000  to  10,000 
5,000  to    7,500 
4,000  to    6,000 

For  a.  newly  designed  machine,  the  value  $'p,  obtained  by 
means  of  formula  (155),  will  be  within  the  limits  given  in  this 

220x10' 


0    200   400    600    800   1000   1200   1-100   1600   1800   2000 

Fig.   131. — Average  Useful  Magnetic  Flux  at  Different  Conductor  Velocities 
for  Various  Outputs. 

table,  provided  the  armature  has  been  calculated  in  accordance 
with  the  rules  and  tables  furnished  in  the  respective  Chapters 
of  Part  II. 


§59] 


USEFUL   AND    TOTAL   MAGNETIC  FLUX. 


213 


As  from  Table  LXII.  follows  the  self-evident  fact  that  the 
magnetic  fields  of  large  dynamos  are  more  efficient  than  those 
of  small  ones,  a  curve  was  plotted  in  order  to  examine  the_rate 
of  this  increase.  For  this  purpose  the  useful  fluxes  of  all  the 
dynamos  considered  were  reduced  to  the  basis  of  a  conductor 
velocity  of  50  feet  per  second,  when  the  heavy  curve,  Fig.  131, 
was  obtained  by  averaging  the  values  of  the  flux  thus  found. 

From  this  curve  a  law  can  be  deduced  for  the  increase  of 
the  field  efficiency  with  increasing  size.  In  the  following 
Table  LXIII.,  from  the  average  useful  flux  for  50  feet  con- 
ductor velocity,  as  plotted  in  Fig.  131,  the  specific  flux  per 
kilowatt  has  been  calculated,  showing  the  rate  of  increase  of 
the  field  efficiency: 

TABLE  LXIII.— VARIATION  OF  FIELD  EFFICIENCY  WITH  OUTPUT 
OF  DYNAMO. 


TOTAL 

SPECIFIC  FLUX, 

CAPACITY 

AVERAGE  USEFUL  FLUX 

IN 

IN 

AT  VELOCITY 

WEBERS  PEJI  KILOWATT, 

KILOWATTS. 

OF 

AT 

50  FEET  PER  SECOND. 

50  FEET  PER  SECOND. 

.1 

100,000 

1,000,000 

.25 

200,000 

800,000 

.5 

350,000 

700,000 

"       1 

600,000 

600,000 

2.5 

1,300,000 

520,000 

5 

2,300,000 

460,000 

10 

4,800,000 

400,000 

25 

8,500,000 

340,000 

50 

15,500,000 

310,000 

75 

22,000,000 

294,000 

100 

28,000,000 

280,000 

200 

50,000,000 

250,000 

300 

70,000,000 

233,000 

400 

88,000,000 

220,000 

500 

104,000,000 

208,000 

600 

118,000,000 

197,000 

700 

130,000,000 

186,000 

800 

141,000,000 

176,000 

900 

151,000,000 

168.000 

1,000 

160,000,000 

160,000 

1,200 

175,000,000 

146,000 

1,500 

195,000,000 

130,000 

2,000 

220,000,000 

110,000 

By  the  law  of  inverse  proportionality  between  useful  flux 
and  conductor  velocity,  the  remaining  curves  for  25,  30,  40,  60, 


214 


DYNAMO-ELECTRIC  MACHINES. 


60 


75,  and  100  feet  per  second,  respectively,  were  then  drawn  in 
Fig.  131. 

Tabulating  all  the  values  thus  received,  we  obtain  the  fol- 
lowing Table  LXIV.,  giving  average  values  of  the  useful  flux 
for  various  conductor  velocities: 

TABLE  LXIV. — USEFUL  FLUX  FOR  VARIOUS  SIZES  OF  DYNAMOS  AT 
DIFFERENT  CONDUCTOR  VELOCITIES. 


AVERAGE  USEFUL  FLUX,  IN  WEBERS,  AT  CONDUCTOR  VELOCITY,  PER  SECOND,  OP: 

CAPACITY 

INT 

KILOWATTS. 

25  feet 

30  feet 

40  feet 

50  feet 

60  feet 

75  feet 

100  feet 

(=  7.5  m.) 

(=  9  m.) 

(=12m.) 

(=15m.) 

(=18m.) 

(=  22.5  m.) 

(=  30  m.) 

.1 

200,000 

167,000 

125,000 

100,000 

83,000 

.25 

400,000 

333,000 

250,000 

200,000 

167,000 

.   .  . 

.5 

700,000 

583,000 

438,000 

350,000 

292,000 

. 

1 

1,200,000 

1,000,000 

750,000 

600,000 

500,000 

400,000 

.   . 

2.5 

2,600,000 

2,200,000 

1,600,000 

1,300,000 

1,100,000 

870,000 

. 

5 

4,600,000 

3,800,000 

2,900,000 

2,300,000 

1,900,000 

1,500,000          .   . 

10 

8,000,000 

6,700,000 

5,000,000 

4,000,000 

3,300,000 

2,700.000 

25 

17,000,000 

14,200,000 

10,600,000 

8,500,000 

7,100,000 

5,700,000 

50 

31,000,000 

25,800,000 

19,400,000 

15,500,000 

12,900,000 

10,300.000 

.   . 

75 

44,000,000 

36,700,000 

27,500,000 

22,000,000 

18,300,000 

14,700,000 

11,000,000 

100 

56,000,000 

46,700,000 

35,000,000 

28,000,000      23,300,000 

18,700,000 

14,000,000 

200 

100,000,000 

83,300,000 

62,500,000 

50,000,000  i     41,700,000 

33,300,000 

25,000,000 

300 

140,000,000 

117,000,000 

87,500,000 

70,000,000 

58,300,000 

46,700,000 

35.000,000 

400 

147,000,000 

110,000.000 

88,000,000 

73,300,000 

58,700,000 

44,000.000 

500 

173,000,000 

130,000,000 

104,000,000 

86,700,000 

68,300,000 

52,000,000 

600 

197,000,000 

148,000,000 

118,000,000 

98,300,000 

78,700,000 

59,000,000 

700 

216,000,000 

163,000,000 

130.000,000 

108,000,000      86,700,000 

65,000.000 

800 

235,000,000 

176,000,000 

141,000,000 

117,000,000      94,000.000 

70,500.000 

900 

189,000,000 

151,000,000 

126,000,000 

101,000,000 

75,500,000 

1,000 

200,000,000 

160,000,000 

133,000,000 

107,000,000 

80,000,000 

1,200 

219,000,000 

175,000,000 

146,000,000  '  117,000,000 

87,500.000 

1,500 

244,000,000 

195,000,000 

163,000,000 

130,000,000 

97.500,000 

2,000 

275,000,000 

220,000,000 

183,000,000 

147,000,000 

110,000,000 

60.  Total  Flux  to  be  Generated  in  Machine. 

The  total  flux  to  be  generated  in  any  dynamo  is  the  product 
obtained  in  multiplying  its  useful  flux  by  the  factor  of  its  mag- 
netic leakage : 

»  =  Ax,  =  AxAx£*_£xj*;      (156) 

$'  =  total  flux  to  be  generated  in  machine,  in  lines  of 

force; 
$  =  useful  flux    necessary   to   produce    the    required 

E.    M.    F.    under  the   given    conditions,    from 

formula  (137); 
A    =  factor    of  magnetic   leakage    (see  Chapters    XII. 

and  XIII). 


£60]  USEFUL   AND    TOTAL   MAGNETIC  FLUX.  215 

The  value  of  the  total  magnetic  flux  in  a  dynamo  directly 
determines  the  sectional  areas  of  the  various  portions  of  the 
magnetic  circuit  in  the  frame  (see  Chapter  XVI.),  and— since 
the  magnetomotive  force  required  depends  upon  the  total 
magnetic  flux  to  be  effected — A  has  a  direct  influence  also 
upon  the  magnet  winding.  In  calculating  a  dynamo-electric 
machine,  therefore,  it  is  of  great  importance  to  compute  the 
actual  value  of  the  total  flux,  and,  consequently,  to  predeter- 
mine with  sufficient  accuracy  the  amount  of  the  magnetic 
leakage. 

But,  since  the  dimensions  of  the  magnetic  circuit  depend 
upon  the  total  flux  to  be  generated,  and  since  the  accurate 
value  of  the  latter  is  given  by  the  coefficient  of  magnetic  leak- 
age which  in  turn  for  a  newly  designed  machine  must  be  calcu- 
lated from  the  dimensions  of  the  magnet  frame,  it  is  necessary 
to  proceed  as  follows: 

An  approximate  value  of  A  for  the  type  and  size  of  dynamo 
in  question  is  taken  from  Table  LXVI1I.,  §  70,  and  the  corre- 
sponding approximate  total  flux  calculated  from  formula  (156). 
With  the  value  of  $'  thus  obtained  the  principal  dimensions  of 
the  magnet  frame  are  determined  according  to  the  rules  given 
in  Chapter  XVI.  The  dimensions  now  being  known,  the 
probable  leakage  factor,  /\,  can  be  figured  from  formula  (157) 
or  (158),  respectively,  §  61,  the  single  terms  of  which  are 
found  from  the  respective  formulae  given  in  Chapter  XII. 

From  formula  (156),  finally,  the  accurate  value  of  the  total 
flux  is  obtained.  Should  the  latter  prove  so  much  different  from 
the  assumed  approximate  value  of  &',  as  to  necessitate  a 
change  in  the  dimensions  of  the  frame,  then  the  calculation  of 
A  will  have  to  be  partly  or  wholly  repeated. 

That  such  a  calculation  of  the  probable  leakage  factor  is 
necessary  in  every  single  case,  is  evident  from  the  fact  that 
not  only  the  leakage  in  two  machines  of  same  general  design, 
and  even  of  approximately  the  same  size,  which  are  merely 
differently  proportioned  in  their  essential  parts,  may  widely 
differ  from  each  other,  but  that  in  one  and  the  same  dynamo 
the  amount  of  the  leakage  can  be  considerably  varied  by  using 
armatures  of  different  core-diameters  in  its  magnetic  field. 

From  the  same  reason  it  can  also  be  concluded  that  the 
method  of  assuming  a  value  of  A  from  previous  experience 


2 1 6  D  YNA  MO-ELECTRIC  MA  CHINES.  [§  6O 

with  a  certain  type,  or  even  with  an  individual  machine,  is  an 
entirely  unreliable  one,  and  that  the  calculation  of  the  mag- 
netomotive force  based  upon  such  an  assumption  cannot  be 
depended  upon. 

The  author's  method  of  predetermining,  from  the  dimen- 
sions of  a  machine,  \ht  probable  factor  of  its  magnetic  leakage 
is  given  in  the  following  Chapter  XII.,  while  a  practical 
method  used  by  the  author  for  computing  the  real  leakage 
coefficient,  from  the  test  of  an  actual  machine,  is  treated  in 
Chapter  XIII. 

Professor  Forbes!  logarithmic  formulae,1  which  are  usually 
given  in  text-books2  for  the  predetermination  of  magnetic 
leakage,  in  the  first  place  are  too  cumbersome  for  the  practical 
electrical  engineer,  and  besides  leave  room  for  doubt  as  to 
their  application  in  special  cases;  Professor  Thompson's  for- 
mula3 for  the  case  of  leakage  between  parallel  cylinders  has 
been  shown4  to  be  incorrect;  and  the  empirical  formulae  given 
by  Kapp  5  for  the  leakage  resistance  of  upright  and  inverted 
horseshoe  types,  although  being  extremely  simple,  have  not 
much  practical  value,  as  they  merely  have  reference  to  the 
size  of  the  machine  and  are  independent  of  the  dimensions  and 
the  design  of  the  field  frame,  and  will  therefore  give  correct 
results  only  in  case  of  dynamos  having  exactly  the  same  rela- 
tive proportions  as  those  experimented  upon  by  Kapp. 

It  is  therefore  believed  that  the  establishment  of  the  geomet- 
rical formulae  presented  in  Chapter  XII.,  which  are  simple  in 
form,  concise  in  application,  and  accurate  in  result,  has  re- 
moved the  principal  difficulties  heretofore  experienced  with 
leakage  calculations. 


1  George  Forbes,  Journal  Society  Telegraph  Engineers,  vol.  xv.  p.  531,  1886. 

2  S.  P.  Thompson,  "Dynamo-Electric  Machinery,"  fifth  edition,  p.  156. 

3  S.  P.  Thompson,  "  Lectures  on  the  Electro-Magnet,"  authorized  American 
edition,  p.  147. 

4 A.    E.    Wiener,    "Magnetic    Leakage  in    Dynamo-Electric   Machinery," 
Electrical  Engineer,  vol.  xviii.  p.  164  (August  29,  1894). 

6  Gisbert  Kapp,  "  Electric  Transmission  of  Energy,"  third  edition,  p.  122. 


CHAPTER   XII. 

CALCULATION    OF    LEAKAGE    FACTOR    FROM    DIMENSIONS 
OF    MACHINE. 

A.  FORMULA  FOR  PROBABLE  LEAKAGE  FACTOR. 

61.  Coefficient  of  Magnetic  Leakage  for  Dynamos  with 
Smooth  and  with  Toothed  or  Perforated  Arma- 
tures. 

Since  air  is  a  conductor  of  magnetism,  the  conditions  of 
the  magnetic  circuit  of  a  dynamo-electric  machine  resemble 
those  of  a  closed  metallic  electric  circuit  immersed  in  a  con- 
ducting fluid.  In  the  latter  case,  the  main  current  will  flow 
through  the  metallic  conductors,  but  a  portion  will  pass 
through  the  fluid.  Similarly,  in  the  dynamo,  the  main  path  for 
the  lines  of  force  being  the  magnetic  circuit  consisting  of  the 
iron  field  frame,  the  air  gaps,  and  the  armature  core,  a  por- 
tion of  the  magnetic  flux  will  take  its  way  through  the  sur- 
rounding air.  The  amount  of  electric  current  passing  through 
the  surrounding  medium,  the  fluid,  depends  upon  the  ratio  be- 
tween the  conductances  of  the  main  to  the  shunt  paths.  In 
order  to  calculate  the  amount  of  magnetic  leakage  in  a  dynamo, 
therefore,  it  is,  analogically,  only  necessary  to  determine  the 
ratio  between  the  permeances  of  the  useful  and  the  stray  paths. 

a.   Smooth  Armature. 

The  leakage  factor  in  any  dynamo  having  a  smooth  arma- 
ture can  accordingly  be  expressed  as  the  quotient  of  the  total 
joint  permeance  of  the  system  by  the  permeance  of  the  useful 
path.  But  since  the  reluctance  of  the  iron  portion  of  the 
main  path  is  very  small  compared  with  that  of  the  air  gaps, 
the  sum  of  their  reciprocals,  that  is,  the  total  permeance  of 
the  useful  path,  is  practically  equal  to  the  permeance  of  the 
gaps;  hence  the  permeance  of  the  gaps  can  be  taken  as  a  sub- 
stitute of  the  permeance  of  the  whole  magnetic  circuit  within 


218  DYNAMO-ELECTRIC  MACHINES.  [§61 

the  machine,  and  we  obtain  the  following  formula  for  the 
probable  leakage  factor  of  any  dynamo  having  a  smooth  arma- 
ture : 

A  —  J°*nt  permeance  of  useful  and  stray  paths 

Permance  of  useful  path 
or, 

*=  *'  +  *•  +  *•+*«,    (157) 

where  ^,  =  relative  permeance  of  the  air  gaps  (useful  path) ; 
^a  =  relative  average  permeance  across  magnet  cores 

(stray  path); 

^$  =  relative  permeance  across  polepieces  (stray  path); 
^4  =  relative  permeance  between  polepieces  and  yoke 

(stray  path). 

The  relative  permeances— by  which  are  understood  the 
absolute  permeances  divided  by  the  magnetic  potential,  and 
which,  therefore,  include  a  constant  factor,  on  account  of  the 
units  chosen — are  taken  for  convenience,  for,  in  each  individ- 
ual case  the  maximum  magnetic  potential  is  the  same  for  all 
permeances,  and  a  constant  numerical  factor,  if  absolute  per- 
meances were  used,  would  be  common  to  all  terms  in  (157), 
and  consequently  would  cancel. 

b.    Toothed  and  Perforated  Armature. 

In  toothed  and  perforated  armatures  a  portion  of  the  magnetic 
lines  of  the  main  path  enters  the  iron  projections  of  the  core 
and  passes  through  the  armature  without  cutting  the  conduc- 
tors. This  portion,  therefore,  cannot  be  considered  as  useful, 
and  has  to  be  taken  into  account  in  computing  the  total  leak- 
age coefficient  of  the  machine.  Introducing  this  leakage  into 
the  calculation  in  the  form  of  a  factor,  the  factor  of  arma- 
ture leakage,  we  obtain  the  probable  leakage  factor  of  any 
dynamo  having  a  toothed  or  perforated  armature: 

V  =  \  x  *  =  \  X  •*'  +  *«+A-+l«.  .      (158) 

The  factor,  \,  of  this  core-leakage,  that  is,  the  ratio  of  the 
total  flux  of  the  useful  path  passing  the  air  gaps  to  the  actual 
useful  flux  cutting  the  armature  conductors,  or  to  the  total  flux 


§  6  2]     PREDE  TERM  IN  A  TION  OF  MA  GNE  TIC  LEA  KAGE.      219 


through  the  gaps  minus  that  portion  leaking  through  the  teeth, 
depends  upon  the  relative  sizes  of  the  slots  to  the  teeth,  and 
for  armatures  otherwise  properly  dimensioned,  has  been  found 
to  average  within  the  following  limits: 

TABLE  LXV. — CORE  LEAKAGE  IN  TOOTHED  AND  PERFORATED 
ARMATURES. 


RATIO  OF 

FACTOR  OP  ARMATURE  LEAKAGE,  Ai 

WIDTH  OF  SLOTS 

TOOTHED  ARMATURES 

PERFORATED  ARMATURES 

ON  OUTER 

STRAIGHT  TEETH 

PROJECTING  TEETH 

RECTANGULAR 
HOLES 

ROUND  HOLES 

CIRCUMFERENCE 

%^%|      fe^^ 

'<%/2%2  ^&///%' 

^tTTf////???*^ 

^^^7^2^n~^^ 

*>*  •  ^/- 

w*%4 

£%>%#%^.. 

&mmz, 

%?%^^ 

0.35 

1.06  to  1.04 

.4 

1.05  "  1.03 

1.10  to  1.04 

.45 

1.04  "  1.02 

1.07  »  1.03 

.5 

1.03  «  1.01 

1.05  "  1.02 

1.07  to  1  04 

1.10  to  1.06 

.55 

1.02  "  1.005 

1.03  "  1.01 

1.06  "  1.03 

1.08  "1.05 

.6 

1.01  "  1.0025 

1.02  "  1.005 

1.05  "  1.02 

1.06  "  1.04 

.65 

1.04"  1.01 

1.05  "  1.03 

.7 

1.03  "  1.01 

1.04  "  1.02 

B.    GENERAL  FORMULA  FOR  RELATIVE  PERMEANCES. 

62.  Fundamental  Permeance  Formula  and   Practical 
Derivations. 

In  order  to  obtain  the  values  of  the  permeances  of  the  vari- 
ous paths,  we  start  from  the  general  law  of  conductance: 

Conductance  =  i  Conductivity  )  Area  of  medium 

(    of  medium    }  Distance  in  medium 


Area 


or,  in  our  case  of  magnetic  conductance: 
Permeance  =  Permeability  x 

Since  the  permeability  of  air  =  i,  the  relative  leakage  per- 
meance between  two  surfaces  can  be  expressed  by  the  general 
formula: 

0_         Mean  area  of  surfaces  exposed  ^IKQ\ 

Mean  length  of  path  between  them  ' 

From  this,  formulae  for  the  various  cases  occurring  in  prac- 
tice can  be  derived. 


220 


DYNAMO-ELECTRIC  MACHINES. 


[§62 


a.    Two  plane  surfaces,   inclined  to  each  other. 

In  order  to  express,  algebraically,  the  relative  permeance  of 
the  air  space  between  two  inclined  plane  surfaces,  Fig.  132, 
the  mean  path  is  assumed  to  consist  of  two  circular  arcs  joined 
by  a  straight  line  tangent  to  both  circles,  said  arcs  to  be  de- 
scribed from  the  edges  of  the  planes  nearest  to  each  other,  as 


Fig.  132. — Two  Plane  Surfaces  Inclined  to  Each  Other. 

centres,  with  radii  equal  to  the  distances  of  the  respective  cen- 
tres of  gravity  from  those  edges.      Hence: 


i  to  +  -S1,) 


(160) 


where   Slt  S  ^  =  areas  of  magnetic  surfaces; 

c   —  least  distance  between  them; 
ai ,  az  =  widths  of  surfaces  St  and  S9,  respectively; 
a  —  angle  between  surfaces  S1  and  S9. 

b.    Two  parallel  plane  surfaces  facing  each  other. 

If  the  two  surfaces  Sl  and  S9  are  parallel  to  one  another, 
Fig.   133,  the  angle  inclosed  is  a  =  o°,  and  the  formula  for 


Fig.  I33-— Two  Parallel  Plane  Surfaces  Facing  Each  Other, 
the  relative  permeance,  as  a  special  case  of  (160),  becomes: 
2  =  *  to  +  *?.).    .., (161) 


§  6  2]     PREDE  TERM  IN  A  TION  OF  MA  GNE  TIC  L  EA  KA  GE.      221 

c.    Two  equal  rectangular  surfaces  lying  in  one  plane. 

In    case    the   two  surfaces    lie    in    the    same    plane,     Fig. 
134,  they  inclose  an  angle  of  a  —  180°,  and  the  permeance~of^ 


Fig.  134. — Two  Equal  Rectangular  Surfaces  Lying  in  One  Plane, 
the  air  between  them,  by  formula  (160),  is: 


a  X  b 


(162) 


a  —  width  of  rectangular  surface; 
b  =  length  of  rectangular  surface; 
c  —  least  distance  between  surfaces. 

d.    Two  equal  rectangles  at  right  angles  to  each  other. 

If  the  two  surfaces  are  rectangular  to  each  other,  Fig.  135, 


trr<*r-n 

Fig.  J35- — Two  Equal  Rectangles  at  Right  Angles  to  Each  Other, 
the  angle  a  —  90°,  formula  (160),   consequently,  reduces  to 

a  X  b 


(163) 


c  +  a  X  - 


e.    Two  parallel  cylinders. 

In  case  the  two  surfaces  are  cylinders  of  diameter,  dt  and 
length,  /,  Fig.  136,  the  areas  of  their  surfaces  are  d  x  TT  X  I; 
and  if  they  are  placed  parallel  to  each  other,  at  a  distance,  c, 
apart,  the  mean  length  of  the  magnetic  path  is  c  -\-  \d;  hence 
the  permeance  of  the  air  between  them: 

9=*^XY.  ..(164) 


222 


DYNAMO-ELECTRIC  MACHINES. 


[§62 


In  this  formula  the  expression  for  the  mean  length  of  the 
path  is  deduced  from  Fig.  137,  in  which  it  is  assumed  that  the 


Fig.  136. — Two  Parallel  Cylinders. 

mean  path  consists  of  two  quadrants  joined  by  a  straight  line 
of  length  <r,  and  extends  between  two  points  of  the  cylinder- 
peripheries  situated  at  angles  of  60°  from  the  centre  line. 

Since  in  an  equilateral  triangle  the  perpendicular,  dropped 
from  any  one  corner  upon  the  opposite  side,  bisects  that  side, 


Fig.  137.  —  Leakage  Path  Between  Parallel  Cylinders. 

the  perpendicular,  from  either  of  the  endpoints  of  the  mean 
path  upon  the  centre  line,  bisects  the  radius  of  the  corre- 
sponding cylinder-circle,  and  the  radius  of  the  leakage-path 
quadrant  is 

d 
=      ; 


hence  the  length  of  the  mean  path: 

x  — 
or,  approximately: 


x  —  c  +y  X  TT  =  c  -f  d  X   - 

4 


This  approximation  even  better  meets  the  practical  truth,  as 
most  of  the  leakage  takes  place  directly  across  the  cylinders. 


§62]     PREDE  TERMINA  TION  OF  MA  GNE  TIC  LEAK  A  GE.      223 

and  the  mean  path,  therefore,  in  reality  is  situated  at  an  angle 
of  somewhat  less  than  60°,  which  was  taken  for  convenience 
in  the  geometrical  consideration. 

f.    Two  parallel  cylinder-halves. 

If  two  cylinder-halves  face  each  other  with  their  curved 
surfaces,  Fig.  138,  the  mean  length  of  the  magnetic  path  is 
c  -f-  -3  d,  where  c  is  the  least  distance  apart  of  the  curved  sur- 


Fig.  138. — Two  Parallel  Cylinder- Halves. 

faces,  and  d  the  diameter  of  the  cylinders,  and  we  have  for  the 
permeance: 


X/ 


2  c  -f  .6  d 


....(165) 


The  mean  length  of  the  path  is  geometrically  found  from 
Fig.  139,  as  follows: 


Fig-  J39- — Leakage  Path  Between  Parallel  Cylinder-Halves. 


224  DYNAMO-ELECTRIC  MACHINES.  [§64 

For,  in  this  case,  the  extent  of  the  leakage  field  is  much 
smaller  than  in  that  of  full  cylinders,  and  the  mean  path  can 
be  assumed  a  straight  line  meeting  the  two  semicircles  at  an 
angle  of  45°  from  the  centre  line. 

C.   RELATIVE  PERMEANCES  IN  DYNAMO-ELECTRIC  MACHINES. 

63.  Principle  of  Magnetic  Potential. 

In  taking  the  magnetic  potential  between  two  polepieces  of 
opposite  polarity  as  unity  for  calculating  the  relative  per- 
meances in  dynamo-electric  machines,  the  potentials  between 
various  points  of  the  magnetic  circuit  depend  upon  the  num- 
ber of  magnet-cores  magnetically  in  series  between  two  con- 
secutive poles  of  opposite  polarity.  If,  as  is  the  case  in  the 
majority  of  types,  there  are  two  magnets  between  any  north- 
pole  and  the  next  south-pole  of  the  machine,  then  the  magnetic 
potential  between  two  points  of  the  magnetic  circuit  separated 
by  but  one  magnet,  is  =  J-;  and  two  points  not  separated 
by  a  magnet  core,  have  no  difference  of  magnetic  potential, 
their  potential  —  o.  If  the  circuit  consists  of  but  one  magnet, 
or  of  several  magnets  magnetically  in  parallel,  then  the  mag- 
netic potential  between  any  two  leakage  surfaces  of  opposite 
polarity  is  =  T,  /.  e.,  the  difference  of  magnetic  potential 
between  the  polepieces. 

The  observance  of  this  general  principle  enables  us  to  bring 
all  the  relative  permeances  into  proper  relation  to  each  other, 
and  we  can  now  apply  formulae  (160)  to  (165)  to  the  cases  of  a 
dynamo. 

04,  Relative  Permeance  of  the  Air  Gaps  (^1). 

a.   Smooth  Armature. 

In  dynamos  with  smooth-core  armatures  the  relative  per- 
meance of  the  air  gaps  simply  is  the  quotient  of  the  mean  field 
area  by  the  mean  length  of  the  lines  in  the  gap-space.  The 
mean  area  of  the  gap-space  for  any  armature  facing  poles 
opposite  its  outer  periphery  is  given  by  formula  (141),  §  57, 
while  the  mean  length  of  the  path,  in  both  gaps,  for  smooth 
armature  cores  is: 

/'*  =  *„  x  K-<4),     (166) 


§  64]     PREDE  TERMINA  TION  OF  MA  GNE  TIC  LEAK  A  GE.      225 

where  k^  is  a  constant  depending  upon  the  degree  of  deflection 
of  the  lines  of  force.  It  is  well  known  that  in  a  dynamo-elec- 
tric machine,  when  the  armature  is  in  motion,  the  lines  clo~not 
cross  the  air  gaps  at  right  angles,  but  are  deflected  into  an  ob- 
lique position,  Fig.  140,  owing  to  the  shifting  of  the  neutral  line. 


Fig.  140. — Deflection  of  Lines  of  Force  in  Gap-Space. 

The  amount  of  this  deflection  naturally  depends  upon  the  speed 
of  the  revolving  armature  and  upon  the  density  of  the  lines,  and 
in  machines  with  smooth-surface  armatures  increases  solely 
with  the  product  of  these  two  quantities: 

TABLE  LXVI. — FACTOR  OF  FIELD  DEFLECTION  IN  DYNAMOS  WITH 
SMOOTH-SURFACE  ARMATURES. 


PRODUCT  OP  CONDUCTOR  VELOCITY  AND  FIELD 

FACTOR  op 

DENSITT,   Vc  X  3C- 

FIELD  DEFLECTION,  ^12  - 

English  Measure. 

Metric  Measure. 

Smooth 

Perforated 

Velocity,  in  feet  per  second. 
Density,  in  lines  per  eq  inch. 

Velocity,  in  metres  per  second. 
Density,  in  lines  per  cm.2 

Armature. 

Armature. 

Below  400,000 

Below  20,000 

1.10 

1.4 

400,000  to      500,000 

20,000  to    25,000 

1.125 

1.45 

500,000          600,000 

25,000         30,000 

1.15 

1.5 

600,000          700,000 

30,000         35,000 

1.175 

1.55 

700,000          800,000 

35,000         40,000 

1.20 

1.6 

800,000          900,000 

40,000         45,000 

1.225 

1.65 

900,000       1,000,000 

45,000         50,000 

1.25 

1.7 

1,000,000       1,100,000 

50,000         55,000 

1.275 

1.75 

1,100,000       1,250,000 

55,000          62,500 

1.30 

1.8 

1,250,000       1,500,000 

62,500          75,000 

1.325 

1.85 

1,500,000       1,750,000     )        75,000         87500 

1.35 

1.9 

1,750.000       2,000,000            87,500        100.000 

1.375 

1.95 

Over  2,000,000 

Over  100,000 

1.40 

2 

226 


D  YNAMO-ELECTRIC  MA  CHINES. 


The  preceding  Table  LXVI.  is  averaged  from  a  great  num- 
ber of  dynamos  under  various  conditions,  and  gives  values  of 
kn  for  smooth  as  well  as  perforated  armatures. 

Combining  formulae  (141)  and  (166),  we  obtain  for  the  case 
of  cylindrical  smooth-core  armatures  with  external  poles: 


7T 

x*x 


i',  x  /, 


X 


-  d&) 


(167) 


in  which  2j  =  relative  permeance  of  air  gaps; 
Sg  =  mean  area  of  gap-space; 
l\  —  mean  length  of  path  in  both  gaps; 
dt  —  mean  diameter  of  magnetic  field, 

=  jK  +  4);      .       "".  ; 

d^  =  diameter  of  armature  core; 
</p  =  diameter  of  bore  of  polepieces; 
/f  =  mean  length  of  magnetic  field, 


See  Fig. 
129, 

page  204. 


/a  =  length  of  armature  core; 

/p  =  length  of  polepieces; 
ft\  =  percentage  of  effective  gap  circumference,  see 

Table  XXXVIII.,  §  38; 
klz  =  factor  of  field  deflection,  Table  LXVI. 

For  armature  revolving  outside  of  a  magnetic  field,  as  in  the 
innerpole  types,  in  the  denominator  of  formula  (167),  the  order 
of  the  diameters  d&  and  dv  is  to  be  reversed,  as  in  this  case  dM 
the  internal  diameter  of  the  armature  core,  is  larger  than  the 
diameter  of  the  pole-bore. 

If  poles  are  situated  interior  as  well  as  exterior  to  the 
armature,  the  mean  of  the  outer  and  inner  gap  areas  has  to  be 
taken  by  applying  formula  (141)  to  the  inner  diameter  as  well 
as  to  the  outer  diameter  of  the  core;  and  instead  of  (</p  —  <4) 
the  sum  of  the  outer  and  inner  gaps  is  to  be  substituted. 
Finally,  in  case  of  armatures  facing  the  poles  in  the  axial 
direction,  as  in  the  flat  ring  armature  type,  the  gap  area,  if 
polepieces  are  used,  is  the  mean  of  half  the  pole  area  and  the 
ring  area  of  the  armature  core;  and  if  no  separate  polepieces 


§  64]     PREDE  TERM  IN  A  T10N  OF  MA  ONE  TIC  LEA  KA  GE.      227 

are  employed,  is  practically  equal  to  half  the  sectional  area  of 
the  magnet  cores.  The  mean  length  of  the  path  is  the  differ- 
ence between  the  axial  pole  distance  and  the  axial  breadth  of 
the  armature  core,  multiplied  by  the  factor  of  field  deflection. 

b.    Toothed  and  perforated  armatures. 

In  machines  with  toothed  and  perforated  armatures  the  air 
gaps  are  composed  of  the  clearance  spaces  between  the  tops  of 
the  iron  projections  and  the  pole  surfaces,  and  of  the  spaces 
between  the  tops  of  the  projections  and  the  bottoms  of  the 


Fig.  141.  —  Gap-Space  of  Toothed  Armature. 

slots;  and  the  relative  permeance  of  the  gaps,  consequently, 
is  the  sum  of  the  relative  permeance  of  the  clearance  spaces 
(•£')  plus  the  relative  joint  permeance  of  the  teeth  ($")  and  of 
the  slots  (^'"),  or,  in  symbols: 


1     "   i  i  $'  -f  3?"  +  $'" 

IF"  <$»  -f  2'" 

The  permeances  of  the  clearance  spaces,  of  the  teeth,  and 
of  the  slots,  respectively,  can  be  expressed,  with  reference  to 
Fig.  141,  as  follows: 

J  K  *  X  A  +  (b,  +  b't)  X  p'«  X  /*',]  X  /, 

*'  =  —  -"  -;     (169) 


228  DYNAMO-ELECTRIC  MACHINES.  [§64 

for  straight  teeth:  ...........     b\  —  -  . 

2 

"  projecting  teeth:  ..........     b\  =  radial  depth  of  tooth 

projection. 
"  perforated  armatures:  ...      (bt  -|-  b't)  x  «'c  =  d'  '&  X  TT  . 

*"  =  d&  n  ~  b*  x  n>c  x  4  x  k,  x  A  x  n  ;    (170) 


(171) 


The  symbols  used  in  these  formulae  are: 

$'    =  relative  permeance  of  clearance  spaces; 
*$"  =  relative  permeance  of  teeth; 
$'"  =  relative  permeance  of  slots; 
d&   =  diameter  at  bottom  of  slots; 
d"&  =  diameter  at  top  of  teeth; 
dv   =  diameter  of  bore  of  polefaces; 
b^    =  breadth  of  armature  slots; 
bt    ~  top  width  of  armature  teeth; 
b\  —  radial  spread  of  magnetic  lines  along  teeth; 
/a    =  length  of  armature  core; 
/f    =  length  of  magnetic  field; 
n'c  =  number  of  armature  slots; 
fil  =  percentage  of  polar  arc, 
«p'x  /?. 

180      ' 

np  =  number  of  pairs  of  poles, 
ft  =  pole  angle; 
fl\  =  percentage   of   effective   gap   circumference,    see 

Table  XXXVIII.,  §  38; 
k^  —  ratio  of  magnetic  to  total  length  of  armature  core, 

Table  XXIIL,  §  26; 
k^—  factor    of    field    deflection,    see    Table    LXVIL, 

below; 
ju  —  permeability  of  iron  in  armature  teeth,  at  density 

employed,  see  Table  LXXV.,  §  81. 

Formulae  (170)  and  (171)  apply  directly  only  to  straight- 
tooth  armatures.  For  projecting  teeth  the  same  formulae,  how- 
ever, can  be  used  if  the  dimensions  of  the  projecting  tooth  are 


§  64]     PREDE  TERM  IN  A  TION  OF  MA  GNE  TIC  LEA  KA  GE.      229 


replaced  by  those  of  a  straight  tooth  of  equal  volume,  as  indi- 
cated by  Fig.  142,  the  reduced  width  of  the  slot,  bSl  ,  taking 
the  place  of  the  actual  width,  £s  .  For/^r/^z/^armature?  with 
rectangular  holes  (Fig.  143)  the  slot  permeance  is  directly 
expressed  by  formula  (171),  while  the  permeance  of  the  iron 
projections  is  equal  to  that  of  straight  teeth  having  equal  vol- 
ume. In  formula  (170),  consequently,  the  reduced  width,  bS}  , 
and  in  (171)  the  actual  width,  6B,  of  the  holes  is  to  be  used. 
For  round  and  oval  perforations,  Figs.  144  and  145,  respect- 
ively, the  iron  projections  being  transformed  into  straight 


Fig.  142.  Fig.  143.  Fig.  144.  Fig.  145. 

Figs.  142   to  145. — Geometrical   Substitution  of  Projecting  Teeth  and   Hole- 
Projections  by  Straight  Teeth  of  Equal  Volume. 

teeth  of  equal  volume,  the  reduced  width,  bSl ,  of  the  perfora- 
tion is  to  be  used  in  both  (170)  and  (171). 

The  permeance  of  the  teeth,  1£",  on  account  of  the  high 
value  of  the  permeability,  /*,  at  even  comparatively  high  satura- 
tion of  the  teeth,  is  very  large  compared  with  the  permeance 
of  the  slots,  2'",  so  that  for  all  practical  purposes  $'"  in  (168) 
may  be  neglected,  and  we  have : 


X 


(172) 


The  permeance  of  the  clearance  space,  2',  furthermore,  is  so 
small  compared  with  2",  that  their  sum  2'  -f-  2*  is  practically 
equal  to  ^",  and  by  canceling  we  obtain  the  approximate 
formula: 


3    =  2' 


(173) 


which  can  be  used  with  sufficient  accuracy  in  all  cases  where 
the  magnetization  in  the  teeth  is  not  driven  beyond  100,000 
lines  per  square  inch  (=  15,500  gausses). 


230 


D  YNA MO-ELECTRIC  MA  CHINES. 


[§64 


Inserting  the  values  from   (109)  into  (173)    we    obtain  for 
straight-tooth  armatures: 


x 


x 


f  or  projecting-tooth  armatures: 


-  K  x  7t  x  A  +  (^ 


«'c  x  A]  x  /f 


*a  x  o 

and  f  or  perforated  armatures: 

7T    , 

63>  4  P 


;  (175) 


i  +  d\  X   ft\)  X  /f 


TABLE  LXVII. — FACTOB  OF  FIELD  DEFLECTION  IN  DYNAMOS 
WITH  TOOTHED  ARMATURES. 


FACTOR  OF  FIELD  DEFLECTION,  fa 

FOK  TOOTHED  ARMATURES. 

RATIO  or 

RADIAL  CLEARANCE 

TO  PITCH  OF  SLOTS 

ON 

Product  of  Conductor  Velocity  and  Field  Density, 
in  English  Measure. 

OUTER  CIRCUMFERENCE. 

500,000 

1,000,000 

1,500,000 

2,000,000  2,500,000 

0.1 

3 

4 

4.75 

5.25           5.5 

.15 

2.65 

3.45 

4.00 

4.40            4.6 

.2 

2.40 

3.05 

3.45 

3.75 

3.9 

.25 

2.20 

2.70 

3.05 

3.25 

3.4 

.3 

2.00 

2.40 

2.75 

2.90 

3 

.35 

1.85 

2.20 

2.50 

2.65 

2.75 

.4 

1.70 

2.00 

2.25 

2.40 

2.5 

.45 

1.65 

1.92 

2.10 

2.25           2.35 

.5 

1.60 

1.85 

2.00 

2.15 

2.2 

.55 

1.55 

1.80 

1.95 

2.05           2.1 

.6 

1.53 

1.75 

1.90           2.00 

2.05 

.65 

1.51 

1.72 

1.87 

1.97 

2.02 

.7 

| 

1.50 

1.70 

1.85           1.95 

2 

The  amount  of  the  field  deflection  in  machines  with  toothed 
armatures  is  primarily  governed  by  the  ratio  of  the  clearance 
space  to  the  pitch  of  the  slots,  and  only  secondarily  depends 
upon  the  ^product  of  conductor  velocity  and  field  density. 


§65]     PREDE  TERM  IN  A  TION  OF  MA  GNETIC  LEAK  A  GE.      23 1 

The  values  for  use  with  formulae  (174)  and  (175)  are  compiled 
in  the  above  Table  LXVIL,  while  those  for  use  with  formula 
(176)  are  contained  in  the  previous  Table  LXVI.  Table 
LXVIL  refers  to  straight  teeth  only;  in  case  of  armatures  with 
projecting  teeth,  the  average  of  the  values  from  Table  LXVIL 
and  from  LXVI.  for  a  corresponding  perforated  armature 
must  be  taken. 

65.  Relative  Average  Permeance  between  the  Magnet 
Cores  (2,). 

Since  in  dynamo-electric  machines  the  magnet  cores,  with 
their  ends  averted  from  the  armature,  are  magnetically  joined 
by  special  "  yokes  "  or  by  the  frame  of  the  machine,  forming 
the  magnetic  return  circuit,  the  magnetic  potential  between 
these  joined  ends  is  practically  =  o,  while  the  full  magnetic 
potential  is  operating  between  the  free  ends  toward  the  arma- 
ture. The  average  magnetic  potential  over  the  whole  length 
of  the  magnet  cores,  therefore,  is*  one-half  of  the  maximum 
potential,  and  the  average  relative  permeance,  consequently, 
one-half  of  that  which  would  exist  between  the  cores,  if  they 
had  the  same  magnetic  potential  all  over  their  length. 

For  the  various  forms  of  magnet  cores,  by  virtue  of  for- 
mulse  (160)  to  (165),  respectively,  we  therefore  obtain  the 
following  relative  average  permeances : 

a.   Rectangular  Cores. 

The  permeance  between  two  rectangular  magnet  cores,  Fig. 
146,  is  the  sum  of  the  permeances  between  the  inner  surfaces 


Fig.  146. — Rectangular  Magnet  Cores. 

which  face  each  other,  formula  (161),  and  between  the  end 
surfaces  which  lie  in  the  same  plane,  formula  (162);  and  there- 
fore the  average  permeance : 


232 


D  YNAMO-ELECTRIC  MA  CHINES. 
<*        *  X  /  +       b  X  I 


2  C 


c       b  X~ 


[§65 

(177) 


where   ay    b,    t,   and   /  are  the  dimensions  of   the    cores    in 
inches,  see  Fig.  146. 

b.   Round  Cores. 

According  to  formula  164,  we  have  in  this  case,  see  Fig.  147 


Fig  147. — Round  Magnet  Cores. 

-  X  /  d  71  X  I 


-  X  - 

2  C 


,     ...(178) 


-d          2  c  -f-  1.5  d 
c.   Oval  Cores. 

For  oval  cores,  Fig.  148,  the  permeance  path  consists  of  two 
parts,  a  straight  portion  between  the  inner  surfaces,  and   a 


Fig.  148. — Oval  Magnet  Cores. 

curved  portion  between  the  round  end  surfaces.     Combining, 
therefore,  formulae  (161)  and  (164),  we  obtain: 


(a  —  £)  X  / 


2   C 


, 


n  X  / 


(179) 


§65]     PREDE  TERMINA  TION  OF  MA  GNE  TIC  LEA KAGE.      233 

d.   Inclined  Cores. 

If  the  cores,  instead  of  being  parallel  to  each  other,  are^afit. 
at  an  angle,  Fig.  149,  the  distance,  <:,  in  formulae  (177),  (178), 


Fig.  149. — Inclined  Magnet  Cores. 

and  (179),  respectively,  has  to  be  averaged  from  the  least  and 
greatest  distance  of  the  cores: 


c  = 


(180) 


t.  Multipolar  Types. 

In  case  of  multipolar  dynamos  of  nv  pairs  of  poles,  the  total 
permeance  across  the  magnet  cores  is  2  «p  times  that  between 
each  pair  of  cores.  In  calculating  the  latter,  it  has  to  be  con- 
sidered that,  while  the  permeance  across  two  opposite  side 
surfaces  of  the  cores  does  not  change  by  increasing  their 
number,  the  leakage  across  two  end  surfaces  is  reduced,  half 
of  the  lines  leaking  to  the  neighboring  core  at  one  side,  and 
half  to  that  on  the  other  side. 

For  rectangular  cores,  therefore,  we  have,  with  reference  to 
Fig  150: 


Fig.  150 — Multipolar  Frame  with  Rectangular  Cores. 


(181) 


234 


D  YNAMO-ELECTRIC  MA  CHINES. 


65 


for  round  cores,  according  to  formula  (165): 

*.  =  --'><;<r^=**T7¥^<«»> 

and  for  oval  cores: 


>-flx/  +  *x..rx,,v     (183) 


In   multipolar  machines,   for  c,   the   smaller  of   either   the 
mean  distance  between  two  magnets,   Fig.   151,   or  twice  the 


Figs.  151  and  152. — Mean  Length  of  Leakage  Path  between  Magnet  Cores 
in  Multipolar  Dynamos. 

mean   distance  between  magnet  core  and  yoke,   Fig.    152,   is 
to  be  taken. 

f.   Iron-clad  Types. 

In  certain  types  of  dynamos,  known  as  "  Iron- clad"  forms 
because  of  their  yokes  constituting  a  complete  encompassment 
around  the  machine,  if  there  are  two  magnet  cores,  they  are 
not  side  by  side  of  each  other,  but  lie  in  line  and  are  faced  by 
the  yokes  connecting  the  same  (Figs.  153  and  155). 

i.    Bipolar  Iron-clad  Type. 

Considering  that  in  the  ordinary  bipolar  iron-clad  type, 
Fig.  153,  the  magnetic  potential  between  the  pole  ends  of  the 


ig-  I53- — Bipolar  Iron-clad  Type. 

cores  is  unity,  between  the  yoke  ends,  however,  is  zero,  and 
at  intermediate  points,  consequently,  is  given  by  the  ratio  of 


§  65]     PREDETERMINA  TION  OF  MAGNETIC  LEAKAGE.      235 


the  distance  from  the  yoke  to  the  entire  length  of  the  core, 
and  further  that  only  half  the  magnetic  potential  exists  be- 
tween the  poles  and  the  yokes,  and  that,  therefore,  the^aver- 
age  potential  between  cores  and  yokes  at  any  point  is  but 
one-quarter  the  maximum  potential  of  the  core  at  that  point, 
we  obtain  the  following  expression  for  the  total  average  per- 
meance between  the  cores: 


X 


1.285 


(184) 


In  this  formula  it  is  assumed  that  leakage  takes  place  in 
three  directions:  (i)  from  magnet  core  to  magnet  core  along 
the  entire  length  of  their  end  surfaces  (parallel  to  the  arma- 


Fig.  154. — Leakage  Paths  in  Bipolar  Iron-clad  Type. 

ture  heads),  paths  /,  /,  Fig.  154,  having  an  average  potential 
half  that  between  the  poles;  (2)  from  core  to  core  across  the 
surfaces  facing  the  yoke  portions  of  the  frame,  along  a  dis- 
tance, from  the  pole  corners,  equal  to  the  distance  c  between 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§65 


cores  and  yokes,  paths  //,  //;  and  (3)  from  the  cores  to  the 
yokes  along  the  remainder  of  the  length  of  the  core-surfaces 
opposite  the  yokes,  paths  ///,  ///. 

From  Fig.  154  the  mean  area  of  these  paths,  ///,  ///,  is  ob- 
tained : 


X  /     = 


X 


TT 


and  the  mean  length: 

I      /  7T  \  I    /  '"\ 

The  magnetic  potential  at  the  leakage  division  point  of  the 


core  is 


/-  c 


the  mean  potentials  of  the  pole  and  yoke  portions  of  the  core 
consequently  are 


respectively,  and  the  average  potentials  of  the  paths  //,  77, 
between  the  pole  portions  of  the  cores,  and  of  the  paths  777, 
777,  between  the  yoke  portions  of  the  cores  and  the  yokes,  are 


respectively. 

2.   Fourpolar  Iron-clad  Type. 

If  the  magnets  are  so  wound  that  consequent  poles  are  pro- 
duced in  the  yokes,  Fig.  155,  then  the  full  magnetic  potential 


Fig.   155. — Fourpolar  Iron-clad  Type. 

prevails  between  the  cores  and  the  yokes,   and  the  average 
potential  along  their  length  is  one-half  the  potential  between 


§  6  5]     PREDE  TERM  IN  A  TION  OF  MA  GNE  TIC  LEA  KA  GE.      237 

the  poles.  For  the  fourpolar  iron-clad  type,  Fig.  155,  having 
two  salient  and  two  consequent  poles,  the  permeance  between 
the  cores  consequently  is: 

^    _  a*  (1  +  m)        b  X  (I  +  **) 

'~ 


Here  all  the  leakage  is  assumed  to  take  place  between  the 
cores  and  the  adjacent  yokes,  for  in  this  type  the  distance,  e, 
between  the  pole-corners  is  generally  not  much  smaller,  if  any, 
than  the  distance,  c9  between  cores  and  yokes,  and  conse- 
quently no  additional  leakage  needs  to  be  considered  at  this 
point,  unless  separate  polepieces  are  used.  See  formula  (196). 

There  being  no  further  stray  paths  in  the  types  considered, 
formulae  (184)  and  (185)  give  the  total  stray  permeances  of  the 
bipolar  and  fourpolar  iron-clad  types,  respectively. 

3.    Single  Magnet  Iron-dad  Type. 

There  being  but  one  magnet  core  in  this  type,  Fig.  156,  the 
stray  paths  from  that  core  to  the  polepiece  of  opposite  polar- 


Fig.  156.  —  Single  Magnet  Iron-clad  Type. 

ity  and  to  the  adjoining  yokes  constitute  the  entire  waste  per- 
meance which  can  be  formulated  as  follows: 

)          (186) 


.g.   Horizontal  Double  Magnet  Type. 

This  type,  Fig.  157,  of  which  the  bipolar  iron-clad  type  can 
be  considered  a  special  case,  concerning  the  magnetic  poten- 


238 


D  YNAMO-ELECTR1C  MA  CHINES. 


[§  66 


tials  of  the  leakage  paths,  has  features  similar  to  the  iron-clad 
form,  and  the  permeance  across  the  magnet  cores  of  the  hori- 


Fig.  157. — Horizontal  Double  Magnet  Type. 

zontal  double  magnet  type,  which,  at  the  same  time  is  its  total 
waste  permeance,  accordingly  can  be  expressed  by  the  formula : 


e  +  b  X  - 


e  +  m  X  - 


X 


'-<•                  (,       Oi) 
— r-±  X  a  Xl  / -)    ( 

^  J_ V          *)    \  ' 

*  M't  4-  A) 


in  which 


is  the  magnetic  potential  at  the  leakage  division  points  of  the 
magnet  cores. 

66.  Relative  Permeance  across  Polepieces  (^,). 

The  amount  of  leakage  across  the  end  and  side  surfaces  of 
the  polepieces,  that  is,  across  all  their  surfaces  not  facing  the 
armature  core,  depends  upon  the  shape  of  the  polepieces  and 
upon  the  design  of  the  machine  with  reference  to  an  external 
iron  surface  (bedplate)  near  the  polepieces. 

For  the  most  usual  shapes  the  following  formulae  can  be  de- 
rived for  the  relative  permeance  across  the  polepieces: 

a.  Polepieces  Having  an  External  Iron  Surface  Opposite  Them. 
i.    Upright  Horseshoe  Type. 

In  the  upright  horseshoe  type,  Fig.  158,  the  entire  direct 
leakage  across  the  polepieces  can  be  assumed  to  pass  through 
the  iron  bedplate,  hence: 


§66]     PREDE TERMINA  7 'ION  OF  MA GNE TIC  LEAKAGE.      239 


...(188)  - 


2   Z 


S  —  half  area  of  iron  surface  facing  polepieces  (centre  por- 
tion of  bedplate),  in  square  inches; 

z  —  distance  from  polepiece  to  iron  surface  (height  of  zinc 
base),  in  inches; 

y,  g,  h  are  dimensions  in  inches,  see  Fig.  158. 


Fig.  158. — Polepieces  of  Upright  Horseshoe  Type. 

2.   Horizontal  Horseshoe  Type. 

In  this  type,  Fig.  159,  the  lines  from  the  lower  halves  of  the 
polepieces  leak- to  the  bedplate,  while  from  the  upper  halves, 
and  from  the  end  surfaces,  they  pass  across  the  pole  gaps: 


Fig.  159.— Horizontal  Horseshoe  Type. 


oj)       


2   Z 


...(189) 


240 


DYNAMO-ELECTRIC  MACHINES. 


[§66 


Sl  =  surface  of  polepiece  opposite  bedplate  (—  half  of  exter- 
nal surface) ; 

*S*3  =  end  surface  of  polepiece; 

S  —  half  area  of  iron  surface  facing  polepieces  (or  area  of 
portion  opposite  one  polepiece). 

3.   Four  polar  Double  Magnet  Type. 

In  machines  of  this  type,  Fig.  160,  there  are   two  leakage 
paths  across  the  polepieces,  the  lines  from  the  lower  pair  of 


7 
Fig.  160. — Fourpolar  Double  Magnet  Type. 

polepieces  passing  across  the  bedplate,  those  from  the  upper 
pair  across  the  pole  gap: 


X 


2  Z 


L (190) 


Since  there  are  no  further  essential  leakages  in  this  type, 
formula  (190)  gives  the  entire  relative  permeance  of  the  waste 
paths  for  the  fourpolar  double  magnet  type. 

b.   Polepieces  Having  No  External  Iron  Surface  Opposite  Them. 

i.   Inverted  Horseshoe  Type  with  Rectangular  Polepieces. 

For  rectangular  polepieces,  Fig.  161,  the  mean  length  of  all 


Fig.  161. — Inverted  Horseshoe  Type  with  Rectangular  Polepieces. 

leakage  paths  are  equal,  and  the  relative  permeance  between 
the  polepieces  may  consequently  be  expressed  by: 


§66]     PREDETERMINATION  OF  MAGNETIC  LEAKAGE.      241 

(191) 


g    X    (/+   2h) 
71 


x 


2.   Inverted  Horseshoe  Type  with  Beveled  or  Rounded  Polepieces. 

In  beveled  and  rounded  polepieces,  Figs.  162  and  163,  re- 
spectively, the  length  of  the  path  across  the  upper  surfaces  is 


Figs.  162  and  163.— Inverted  Horseshoe  Type  with  Beveled  and  Rounded 

Polepieces. 

somewhat  smaller  than  that  of  the  side  surfaces,  and  the  per- 
meance formula  consists  of  two  terms: 


».= 


x 


2ft  x  > 


7T  7T 

*  x  -       '  +  5-X  — 


..(192) 


3.    Single  Magnet  Type. 

Here  there  are  four  distinct  paths  for  the  leakage  lines  from 
polepiece  to  polepiece,  viz.,  across-  the  end  surfaces  of  the 


Fig.  164. — Single  Magnet  Type. 


yoke  portions,  the  end  surfaces  of  the  pole  portions,  the 
facing  surfaces  of  the  pole  portions,  and  the  inside  projections 
of  the  pole  portions;  hence  we  obtain,  with  reference  to 
Fig.  164: 


242 


D  YNAMO-ELECTRIC  MA  CHINES. 
r  X  h 


[§66 


4_ 


All  leakage  paths  of  the  single  magnet  type  being  considered 
in  this  formula,  (193)  gives  the  total  relative  permeance  of  the 
waste  field  of  that  type. 

4.  Double  Magnet  Type. 

There  is  no  leakage  between  the  magnet  cores  nor  between 
polepieces  and  yoke  in  this  type,  the  total  stray  permeance  of 


Fig.  165.  —  Double  Magnet  Type. 

the  double  magnet  type,  Fig.  165,  therefore,  is  given  by  the 
formula  : 


2.= 


r 


?].     (194) 


/  '    e  +  /. 

5.   Double  Horseshoe  Type. 

In  the  double  horseshoe  type,   Fig.  166,   the  only  leakage 
across  the  polepieces  takes  place  at  the  end  surfaces  and  at 


Fig.  166.— Double  Horseshoe  Type. 

the  pole  corners,  hence  we  have  for  this,  and  for  similar  sym- 
metrical bipolar  types: 


§66]     PREDETERMINATION  OF  MAGNETIC  LEAKAGE.      243 

»X/ 


=    2    X 


; 


/x/ 

e 


(195) 


6.   Iron-clad  Type. 

In  iron-clad  types,  Fig.  167,  the  leakage  from  the  end  sur- 
faces and  the  back  surface  of  the  polepieces  takes  place  to  the 


Fig.  167.  —  Iron-clad  Type. 

yoke,  see  formula  (204)  ;  for  the  permeance  across  the  pole- 
pieces,  only  the  side  surfaces  are  to  be  considered,  and  we 
obtain: 

h  x 


x 


(196) 


7.  Radial  Multipolar  Type. 

In  radial  multipolar  dynamos,  Fig.  168,  lines  pass  from  the 
end  surfaces  of  the  polepieces  across  the  pole  gaps: 


Fig.  168.— Radial  Multipolar  Type. 


..(197) 


=  number  of  pairs  of  magnet  poles. 


244  DYNAMO-ELECTRIC  MACHINES.  [§67 

8.    Tangential  Multipolar  Type. 

The  leakage  between  adjacent  polepieces  in  tangential  mul- 
tipolar  machines,  Fig.  169,  takes  place  across  the  length  of  the 
magnet  cores: 


Fig.  169. — Tangential  Multipolar  Type. 


Sl  =  half  area  of  external  surface  of  polepiece; 
S^  =  area  of  side  surface  of  polepiece; 
iS",  =  area  of  projecting  portion  of  end  surface,  =  end 
surface  —  area  of  magnet  core. 

67.  Relative  Permeance  between  Polepieces  and  Yoke 
PW- 

According  to  the  general  principle  of  calculating  relative 
permeances,  the  magnetic  potential  between  polepieces  and 
yoke  is  to  be  taken  =  ^  with  reference  to  the  potential  be- 
tween two  polepieces  of  opposite  polarity.  For,  the  yokes 
serve  to  join  two  magnet  cores  in  series,  magnetically,  and  are 
therefore  separated  from  the  polepieces  by  but  one  magnet 
core.  If  the  yokes  join  the  magnets  in  parallel,  then  they 
usually  serve  as  polepieces  also,  and  must  be  considered  as 
such  in  leakage  calculations. 

Since  the  amounts  of  the  leakages  in  the  various  paths  are 
proportional  to  their  permeances,  in  dynamos  having  an  ex- 
ternal iron  surface  near  the  polepieces,  most  of  the  leakage 
takes  place  between  the  polepieces  through  that  external  sur- 
face; and  in  such  machines  the  leakage  from  the  polepieces  to 
the  yoke  is  comparatively  small. 


§  6  7]     PREDE  TERM  IN  A  TION  OF  MA  GNE  TIC  LEA  KA  GE.      245 
a.   Polepieces  Having  an  External  Iron  Surface  Opposite  Them. 

i.    Upright  Horseshoe  Type. 

From  the  polepiece  area  facing  the  yoke,  ,S3,  Fig.   170,  the 
leakage  takes  place  in  a  straight  line  equal  in  length  to  that  of 


Fig.  170. — Upright  Horseshoe  Type. 

the  magnet  cores,  while  from  the  end  surfaces   the  leakage 
paths  are  quadrants  joined  by  straight  lines: 


S3  =  projecting  area  of  polepiece,  =  top  area  of  pole- 
piece  minus  area  of  magnet  core. 

2.   Horizontal  Horseshoe  Type. 

The  leakage  from  the  polepieces  to  the  yoke  partly  passes 
directly  across  the  cores,  and  partly  takes  its  path  through  the 
iron  bed;  hence,  with  reference  to  Fig.  159,  page  239,  we  have 
approximately: 

34  =  f  •  +  s* (200) 

•Sj  —  half  area  of  external  surface  of  polepiece; 
S3  =  projecting  area  of  polepiece,  =  area  of  yoke-end 
of  polepiece  minus  area  of  magnet  core; 

/  =  length  of  magnet  core; 

z  =  distance  of  polepiece  from  iron  bedplate. 


246 


DYNAMO-ELECTRIC  MACHINES. 


[§67 


b.   Polepieces  Having  No  External  Iron  Surface  Opposite  Them. 
i.    Inverted  Horseshoe  Type  with  Rectangular  Polepieces. 

In  this  case  the  leakage  from  the  side  surfaces  of  the  pole- 


Fig.  171.— Inverted  Horseshoe  Type  with  Rectangular  Polepieces. 
pieces  to  the  yoke,  Fig.  171,  is  twice  that  of  the  upright  type 

2>4  =  4'+  -    fXk (201) 


2.   Inverted  Horseshoe  Type  with  Beveled  or  Rounded  Polepieces. 

Similar  to  the  former  case  we  have  for  these   forms  of  the 
polepieces,  Figs.  172  and  173,  respectively: 


Figs.  172  and  173. — Inverted  Horseshoe  Type  with  Beveled  and  Rounded 

Polepieces. 

$=^  +       /*»       (202) 


3.   Horizontal  Double  Magnet  Type. 

If  in  this  type  special  polepieces  are  applied,  Fig.  174,  lines 


Fig.  174. — Horizontal  Double  Magnet  Type. 

pass  from  the  lower  surfaces  of  the  same  to  the  yoke: 


§67]     PREDETERMINATION  OF  MAGNETIC  LEAKAGE,      247 


| 


....(203) 


Here  it  is  supposed  that  the  path  from  the  projecting  back 
surfaces  of  the  polepieces  to  the  yoke  below  them  is  shorter 
than  the  length  of  magnet  cores;  if  the  latter  is  not  the  case, 
the  term 


in  the  denominator  of  the  second  portion  of  formula  (203)  is 
to  be  replaced  by  /,  the  length  of  the  cores. 

4.   Iron-clad  Types. 

In  the  bipolar  iron-clad  type,  with  separate  poleshoes,  Fig. 
175,  lines  leak  to  the  yoke  from  the  back  surfaces  of  the  pole- 


Fig.  175. — Bipolar  Iron-clad  Type  with  Poleshoes. 

pieces;  hence  the  relative  permeance,   half  of  the  total  mag- 
netic potential  existing  between  polepieces  and  yoke: 

.  (204) 


7t 

4 

As  to  the  denominator  of  the  second  term,  see  remark  to 
formula  (203). 

This  amount,  formula  (204),  as  well  as  the  relative  permeance 
across  the  side  surfaces  of  the  polepieces,  formula  (196),  is  to 
be  added  to  the  relative  permeance  found  by  formula  (184), 
iron-clad  type  without  polepieces,  in  order  to  obtain  the  total 
relative  permeance  of  this  type. 

In  the  fourpolar  iron-clad  type,  since  the  total  magnetizing 
force  of  each  circuit  is  supplied  by  one  magnet  only,  there  is 


248  DYNAMO-ELECTRIC  MACHINES.  [§68 

full  magnetic  potential  between  polepieces  and  frame,  and  both 
terms  of  formula  (204)  must  consequently  be  multiplied  by  2. 
5.   Radial  Multipolar  Type. 

In  this  type  leakage  lines  pass  from  the  projecting  portions, 
,£3,  Fig.  176,  of  the  back  surfaces  of  the  polepieces  to  those  of 


Fig.  176. — Radial  Multipolar  Type. 

the  yoke,  S^,  and  if  the  yoke  is  relatively  near  to  the  pole  gap, 
leakage  also  takes  place  from  the  end  surfaces  of  the  polepieces 
to  the  yoke: 


X 


A^  +  ^)  +  f/JLgY 


...(205) 


According  to  the  design  of  the  frame,  then,  either  formula 
(205)  is  to  be  used  together  with  the  latter  portion  of  formula 
(197),  or  the  entire  formula  (197)  is  to  be  combined  with  the 
first  portion  of  formula  (205),  in  order  to  obtain  the  total  joint 
permeance  across  the  polepieces  and  from  polepieces  to  yoke 
of  the  radial  multipolar  type. 

By  the  proper  combination  of  formulae  (167)  to  (205)  the 
probable  leakage  factor  of  any  dynamo  can  be  calculated  from 
the  dimensions  of  the  machine. 

D.    COMPARISON  OF  VARIOUS  TYPES  OF  DYNAMOS. 

68.  Application  of  Leakage  Formulae  for  Comparison 
of  Tarious  Types  of  Dynamos. 

In  order  to  illustrate  the  application  of  the  above  for- 
mulae, and  at  the  same  time  to  afford  the  means  of  comparing 
the  relative  leakages  in  various  well-known  types  of  dynamos, 
in  the  following,  frames  of  various  types  are  designed  for  the 
same  armature,  and  the  leakage  factor  for  each  machine  thus 
obtained  is  calculated. 


68]     PREDE  TERMINA  TION  OF  MA  GNE  TIC  LEAK  A  GE.      249 


In  order  to  accommodate  all  the  types  to  be  considered  here, 
the  armature  has  been  chosen  of  a  square  cross-sectioirpm.,- 
16  inches  core  diameter,  and  16  inches  long.     This  armature, 
if  wound  to  a  height  of  about  £  inch,  and  driven  at  a  speed  of 
800  revolutions  per  minute,  will  yield  an  output  of  50  KW. 

The  polepieces  for  this  armature  must  have  a  bore  of  iy£ 
inches,  and  must  be  16  inches  long;  the  pole  angle,  for  all 
bipolar  types,  is  chosen  ft  =  136°.  and  the  distance  between 
the  pole  corners,  therefore,  is  17^  X  sin  £  (180°  —  136°)  —  6£ 
inches. 

Figs.  177  to  186  give  the  dimensions  of  various  types  of 
frames  for  this  armature,  viz.,  (i)  Upright  Horseshoe  Type; 


.ins, 


Fig.  177. — Upright  Horseshoe  Type. 

(2)  Inverted  Horseshoe  Type;  (3)  Horizontal  Horseshoe 
Type;  (4)  Single  Magnet  Type;  (5)  Vertical  Double  Magnet 
Type;  (6)  Vertical  Double  Horseshoe  Type;  (7)  Horizontal 
Double  Horseshoe  Type;  (8)  Horizontal  Double  Magnet  Type; 
(9)  Bipolar  Iron-clad  Type;  and  (10)  Fourpolar  Iron-clad 
Type,  respectively. 

The  probable  leakage  factors  of  these  machines  figure  out 
as  follows: 

i .    Upright  Horseshoe  Type,  Fig.  777. 
By  (167): 


16 


1-3°  X   (175   -  16) 


=  3ZS_ 
'•95 


25°  DYNAMO-ELECTRIC  MACHINES. 

By  (178): 


[§68 


—  14    X    7T    X    20  __   43.98    X    20 


2  X 
By  (188): 


1.5  X  H  15 


_ 

24'5' 


X  (i2j  +  8-|)  +  300]  _ 
2  x  5 


(199): 


16  x 


=  4-3  +  3-3  =  7-6. 


X 


By  (157): 

A  =  T92  +24.5  +  29.1  +  7.6  _  253.2   = 
i92  192 

2.    Inverted  Horseshoe  Type,  Fig.  178. 


Fig.  178.—  Inverted  Horseshoe  Type, 
=  192. 

=  24.5- 
By  (192): 

-          6i  X  16  2  X  i7i  X  7 

.  *  —  -+  -  ^-  =  6.2  +  9.4^:15.6. 


By  (202): 

85  16  X   nj 


=  4-3  +  4-9  -  9-2. 


20 


§  68]     PREDE  TERMINA  TION  OF  MA  GNE  TIC  LEAK  A  GE.      25  1 

By  (157): 


A  = 


9-2  _ 


192  192 

3.   Horizontal  Horseshoe  Type,  Fig.  179. 


l 


Fig.  179. — Horizontal  Horseshoe  Type. 


2,  =  192. 

»,  =  24-5- 
By  (189): 


By  (200): 

I4    X 


A  =  i92  +  24.5  +  53-3  +  27.6 
192 

4.   Single  Magnet  Type,  Fig.  180. 
^  —  192. 
By  (193): 


297.4 
192 


6yt 


252 


DYNAMO-ELECTRIC  MACHINES. 


[§68 


192 


192 


Fig.  180.  —  Single  Magnet  Type. 
5.    Vertical  Double  Magnet  Type,  Fig.  181. 


!«— -  —-40& ^ 

Fig.  181. — Vertical  Double  Magnet  Type. 

a,  =  192. 

By  (194): 

2   .     2  v    j  (49J+  16)  X  7 +  (228.5  ~  78.5)    ,    i6X4J 
(  16 

=  2  (38.2  +  6.8)  =  90. 

^  _  192  +  90   __  282  =  ^  ^ 
192  192 

6.    Vertical  Double  Horseshoe  Type,  Fig.  182. 
^  =  192. 

By  (177): 
«>    .  .   14  x  16 


2    X 


^  29.9 


.1=  41. 


§68]    PREDETERMINATION  OF  MAGNETIC  LEAKAGE.      253 

By  (195): 


=  »' 


x 


=  2  X  (4-6  +  1.6  -f-  i.i)  =  14.6. 


Fig.  182.— Vertical  Double  Horseshoe  Type. 

By  (201): 

>   -  -   (16  X  6f  -  14  X  5|)  +  i4  X  3j   ,  16  X 


=  5  -h  10.2  =  15.2. 
X  =  T92  +  4i  +  J4-6  +  I5-2  _  262.8 

7.   Horizontal  Double  Horseshoe  Type,  Fig.  183. 

X^'  V^l  ^S;M  80-8  «l.  ins. 


Fig.  183.  —  Horizontal  Double  Horseshoe  Type. 


,  -  192. 
By  (179): 


16    .    6  X  7t  X  16 
7i  +  i-  X  6 


=  '9-3  +  2S-7  =  45- 


254 


DYNAMO-ELECTRIC  MACHINES. 


[§ea 


4j  X   I7j  I  X   16  j  X   16 


=  2  x  (4-6  -j-  1.6  4-  .6)  =  13.6. 
By  (201): 

_  (16  X  6f  -  80.8)  4-  25  X  16 


16 

X   - 


*-+, (.- 


+- 


16  +  11  X  18 


45 


=  14.2  4-  4.45  4-  6. 15  =  24.8. 


_  275.4 


8.   Horizontal  Double  Magnet  Type,  Fig.  184. 


Fig  184.—  Horizontal  Double  Magnet  Type. 


,  =  192. 
By  (187): 


X 


X 


H+  25*  X- 
16  X  7         ,    1    y     I0ix     I6><   H 

-T-          I          "2          ^  T    "    1 


=  8-5  +  5-1  -h  5-1 


192    +   31 


192  192 


5i 


§  6  8]     PREDE  TERM  IN  A  TION  OF  MA  GNE  TIC  LEA  KA  G£.      255 
9.   Bipolar  Iron-clad  Type,  Fig.   185. 


2,  =  I92. 
By  (184): 


Fig.  185.— Bipolar  Iron-clad  Type. 


I6x 


i7i  1.285    X    5^  ' 

_    I92    +   30  222 

^T"    =  192  ==  L15- 

10.   Fourpolar  Iron-clad  Type,  Fig.  186. 


7'9 


Fig.  1 86. — Fourpolar  Iron-clad  Type. 


By  (167): 


16  7f  -f  lyj  n  X   —    r  X   16 
9°°  >  339 


By(!85): 


DYNAMO-ELECTRIC  MACHINES. 


[§68 


16  X 


, 
r 


8}  X 

- 


=  174+  107.8 
174 


=  88.8 

281.8 

174 


19  =  107.8. 


Taking  now  the  leakage  proper,  that  is,  leakage  factor 
minus  i,  of  the  bipolar  iron-clad  type,  which  is  the  smallest 
found,  as  unity,  we  can  express  the  amounts  of  the  stray  fields 
of  the  remaining  types  as  multiples  of  this  unity,  thus  obtain- 
ing the  following  comparative  leakages  of  the  types  consid- 
ered : 


Upright  horseshoe  type 0.32 

Inverted  horseshoe  type °-255 

Horizontal  horseshoe  type 0.55 

Single  magnet  type 0.32 

Vertical  double  magnet  type   0.47 

Horizontal  double  horseshoe  type..   0.37 

Vertical  double  horseshoe  type 0.43 

Horizontal  double  magnet  type....   o.  16 

Bipolar  iron-clad  type   o.  15 

Fourpolar  iron-clad  type 0.62 


o.  15  =  2.14 
0.15  =  1.70 

0.15  =  3-67 
0.15  =  2.13 

0.15  =  3-i3 

o.  15  =  2.46 

0.15  =  2.87 

0.15  =  1.07 

0.15  =  i 

0.15  =  4.14 


If,  in  the  latter  machine,  the  stray  field  of  which  is  some- 
what excessive,  an  armature  of  larger  diameter  and  smaller 
axial  length  would  be  chosen  and  the  dimensions  of  the  frame 
altered  accordingly,  the  leakage  would  be  found  within  the 
usual  limits  of  the  fourpolar  iron-clad  type. 


CHAPTER   XIII. 

CALCULATION    OF     LEAKAGE    FROM    MACHINE    TEST. 

69.  Calculation  of  Total  Flux. 

The  machine  having  been  built,  its  actual  leakage  can  be 
determined  from  the  ordinary  machine  test.  It  is  only  neces- 
sary, for  this  purpose,  to  run  the  machine  at  its  normal  speed, 
and  to  regulate  the  field  current — by  changing  the  series-regu- 
lating resistance  in  a  shunt  dynamo,  or  by  altering  the  num- 
ber of  turns  in  a  series  machine,  or  by  regulating  both  in  a 
compound-wound  dynamo — until  the  required  output  is  ob- 
tained. Noting  then  the  exciting  ampere-turns,  we  can  calcu- 
late the  total  magnetic  flux,  <£',  through  the  magnet  frame,  by 
a  comparatively  simple  method  which  is  given  below;  and  <&' 
divided  by  the  useful  flux,  $,  gives  the  factor  A  of  the  actual 
leakage. 

The  observed  magnetizing  force  of  AT  ampere-turns  per 
magnetic  circuit — made  up  of  Tsh  shunt  turns,  through  which 
a  current  of 

£ 

A*  -       ~  amperes 

^m 

(E  —  potential  at  terminals,  rm  =  total  resistance  of  shunt 
circuit)  is  flowing,  in  a  shunt  machine;  or  of  Tse  series  turns 
traversed  by  a  current  of  7se  =  /  amperes  (/  =  current  output 
of  dynamo),  in  a  series  machine;  or  partly  of  the  one  and 
partly  of  the  other,  in  a  compound  dynamo —  is  supplying  the 
requisite  magnetizing  forces  used  in  the  different  portions 
of  that  circuit,  viz.,  the  ampere  turns  needed  to  overcome  the 
magnetic  resistance  of  the  air  gaps,  of  the  armature  core,  and 
of  the  field  frame,  and  the  magnetizing  force  required  to 
compensate  the  reaction  of  the  armature  winding  upon  the 
magnetic  field;  hence  we  have: 

AT  =  atK  +  at&  +  atm  +  att,     (206) 

257 


258  DYNAMO-ELECTRIC  MACHINES.  [§69 

where  AT  —  total    magnetomotive  force   required    per   mag- 

netic  circuit  for   normal    output,  in   ampere- 

turns,  observed; 
atg    —  magnetomotive  force  used  per  circuit  to  over- 

come the  magnetic  resistance  of  the  air  gaps 

in  ampere-turns,  see  §  90; 
at&    =  magnetomotive  force  used  per  circuit  to  over- 

come magnetic  resistance  of  armature  core  in 

ampere-turns,  see  §  91; 
atm  —  magnetomotive  force  used  per  circuit  to  over- 

come magnetic  resistance  of  magnet  frame,  in 

ampere-turns,  see  §  92; 
atr    —  magnetomotive  force  required   per   circuit   for 

compensating  armature  reactions,  in  ampere- 

turns,  see  §  93. 

Since  the  magnet  frame  alone  carries  the  total  flux  gen- 
erated in  the  machine,  while  the  air  gaps  and  the  armature 
core  are  traversed  by  the  useful  lines,  only  the  ampere-turns 
used  in  overcoming  the  resistance  of  the  magnet  frame  depend 
upon  the  total  magnetic  flux,  and  all  others  of  these  partial 
magnetomotive  forces  can  be  determined  from  the  useful  flux. 
The  latter,  however,  is  known  from  the  armature  data  of  the 
machine  by  virtue  of  equations  (137)  and  (138),  respectively; 
consequently,  from  (206)  we  can  determine  atm,  and  this,  in 
turn,  will  furnish  the  value  of  the  total  flux,  $'. 

Transposing  (206),  we  obtain: 


-  (ate  +  ta&  +  atr),      .....  (207) 


in  which  AT  is  known  from  the  machine  test,  atg  and  atA 
can  be  calculated  from  the  useful  flux,  and  atr  is  given  by  the 
data  of  the  armature. 

The  numerical  value  of  atm  having  been  found,  we  can 
then  calculate  the  total  magnetic  flux  through  the  machine. 
In  the  following,  the  two  cases  occurring  in  practice  are  con- 
sidered separately,  viz.  :  (i)  but  one  material,  and  (2)  two 
different  materials  being  used  in  building  the  magnet  frame  of 
the  machine. 


§  69]     CALCULA  T10N  OF  AC  TUAL  MA  GNE  TIC  LEAK  A  GE.      259 

a.  Calculation  of  Total  Flux  when  Magnet  Frame  Consists  of  but 
One  Material. 

If  but  one  single  material — either  cast  iron,  wrought  iron, 
mitis  metal,  or  steel — is.  used  in  the  magnet  frame,  the  calcu- 
lation of  the  total  magnetic  flux  is  a  very  simple  operation. 

For,  if  /"m  denotes  the  length  of  the  magnetic  circuit  in  the 
magnet  frame,  from  air  gap  to  air  gap,  and  (B"m  is  the  cor- 
responding mean  specific  magnetization,  then,  according  to 
formula  (226),  §  88, we  have: 

*/„  =  /"*  X /((&'„) (208) 

But  the  density  in  the  magnet  frame,  (B"m,  is  the  quotient  of 
the  total  flux  per  magnetic  circuit,  <£" ,  by  the  mean  sectional 
area,  »Sm,  of  one  magnetic  circuit  in  the  field  frame,  con- 
sequently: 


«/m  =  /'m   X  / 

from  which  follows: 


(D 


L 


(209) 


Dividing  the  numerical  value  of  #/m,  as  found  by  formula 
(207),  by  the  length,  l"m  ,  of  the  circuit,  we  therefore  obtain 
the  numerical  value  of  the  specific  magnetizing  force  per  inch 
length  for  the  respective  material.  By  means  of  Table 
LXXXVIIL,  or  Fig.  256,  then,  the  density  &"m  ,  corresponding 
to  this  particular  value  of  /  ((B"m)  for  the  material  employed, 
can  be  found;  and  since 


we  obtain  the  total  magnetic  flux  per  magnetic  circuit  of  the 
machine  from  the  simple  formula 

0'  =  SmX  (B*m,      ...  ..........  (210) 

where  Sm    =  mean  sectional  area  of  magnet  frame,  in  square 

inches; 

(B"m  =  density  of  lines  of  force  in  magnet  frame,  corre- 
sponding to  the  value  of  atm  -=-  l"m  in  Table 
LXXXVIIL,  or  in  Fig.  256. 


260  DYNAMO-ELECTRIC  MACHINES.  [§69 

b.    Calculation  of  Total  Flux  when  Magnet  Frame  Consists  of  Two 
Different  Materials. 

In  magnet  frames  made  up  of  two  different  materials  — 
either  of  wrought  iron  cores  and  cast  iron  yokes  and  pole- 
pieces;  or  of  wrought  iron  cores  and  yokes,  and  cast  iron  pole- 
pieces;  or  of  any  other  combination  of  two  of  the  various 
kinds  of  iron  in  use  for  this  purpose  —  the  calculation  of  the 
total  magnetic  flux  is  performed  by  an  indirect  method. 

Let  us  assume  that  the  two  materials  used  are  wrought  and 
cast  iron,  and  consequently  denote 

by  ^w.i.  tne   length  of  one  circuit  in  the  wrought  iron  portion 

of  the  frame,  in  inches; 
"     ^"c.i.  the  length  of  one  circuit  in  the  cast  iron  portion  of  the 

frame,  in  inches; 
"  SwAt  the  mean  area  of  one  circuit  in  the  wrought  iron  por- 

tion, in  square  inches; 
"     Sc  j  the  mean  area  of  one  circuit  in  the  cast  iron  portion,  in 

square  inches; 
"(B"w.  i.  the  average  magnetic  density  in  the  wrought  iron,  in 

lines  of  force  per  square  inch;  and 
"  &"C.L  tne  average  magnetic  density  in  the  cast  iron,  in  lines 

of  force  per  square  inch  ; 
then  we  have  the  equation: 

«/m  =  '"w.I.    X  /  (<B"w.i.)  +  /"c.i.    X  /  (CB"e.L)  ' 


or,  by  comparison  with  formula  (207)  : 


tT)  .........  (212) 

This  equation  contains  two  unknown  quantities,  viz.  : 


§  70]     CALCULA  TION  OF  ACTUAL  MA  GNE  TIC  LEAK  A  GE.      261 

and  can,  consequently,  not  be  solved  directly.  Table 
LXXXVIIL,  however,  affords  the  means  of  calculating  3>"  in 
an  indirect  manner,  as  follows: 

The  usual  flux,  <£,  being  known  by  virtue  of  formula  (137) 
or  (138),  respectively,  an  assumption  can  be  made  of  the  total 
flux  per  circuit,  $",  by  adding  to  the  usual  flux  per  circuit, 


(nz  being  the  number  of  the  magnetic  circuits  in  the  ma- 
chine), from  10  to  100  per  cent.,  according  to  the  size  and  the 
type  of  the  dynamo  (see  Table  LXVIII.).  In  dividing  this 
approximate  value  of  3>"  by  the  areas  vSw  L  and  ScA  ,  respect- 
ively, the  densities  (B"w.  i.  and  ®>"c.\.  are  obtained,  and  by  means 
of  Table  LXXXVIIL  (Fig.  256)  the  corresponding  value  of 
/  (®"w.  0  and/  (®"C.L)>  respectively.  Introducing  these  values 
in  the  equation 


($" 
3^ 


a  value  Z  is  produced  which,  in  general,  will  differ  from  the 
value  atm  obtained  by  formula  (207). 

If  Z  is  found  smaller  than  the  actual  value  of  atm  ,  then  the 
value  of  4>*  was  assumed  too  small;  if  larger,  then  £>"  was 
taken  too  large.  A  second  assumption  of  3>"  is  now  made  so 
that  the  corresponding  value  of  Z  obtained  in  a  similar  manner 
from  Table  LXXXVIIL  and  formula  (213)  will  be  on  the 
other  side  of  #/m,  /".  <?.,  larger  than  atm  in  the  former,  and 
smaller  in  the  latter  case. 

By  properly  interpolating  between  the  first  and  second 
assumption,  a  third  assumption  of  <&"  is  now  made  which  will 
produce  a  value  of  Z  very  near  the  actual  value  of  atm.  A 
fourth,  or  eventually  a  fifth  assumption,  will  then  make  the 
value  of  Z  practically  equal  to  atm  from  formula  (207),  and  that 
final  value  of  $",  which  satisfies  the  equation  (212),  is  the  re- 
quired total  flux  per  magnetic  circuit  of  the  dynamo. 

70.  Actual  Leakage  Factor  of  Machine. 

Being  thus  able  to  calculate  the  total  flux  of  magnetic  lines 
through  any  dynamo  from  the  ordinary  machine  test,  that  is? 


262  D  YNA  MO-ELE  C  TRIG  MA  CHINE  S.  [§70 

from  its  ordinary  running  conditions,  the  actual  factor  of  mag- 
netic leakage  can  be  found  from 


where     0'  =  total    flux    through    magnet    frame,    in    lines   of 

force; 
3>"  =  total  flux  per  magnetic  circuit,  calculated  from 

formula  (210),  or  (212),  respectively; 
$  =  useful  flux    cutting  armature    conductors,*  from 

(137)  or  (138),  respectively; 
nz  =  total  number  of  magnetic  circuits  in  machine. 

The  author,  by  employing  his  method  of  calculating  the  leak- 
age from  the  ordinary  machine  test,  §'69,  has  figured  the  leakage 
factors  for  a  great  number  of  practical  dynamos1  of  which  the 
test  data  were  at  his  command,  and  by  combining  his  results 
with  the  researches  of  Hopkinson,2  Lahmeyer,3  Corsepius,4 
Esson,5  Wedding/'  Ives,7  Edser,8  and  Puffer,9  has  averaged  the 
following  Table  LXVIII.  of  leakage  factors  for  dynamos  of 
various  types  and  sizes,  which  is  intended  as  a  guide  in  making 
the  first  assumption  of  the  total  flux,  for  solving  equation  (212), 
as  well  as  for  dimensioning  the  field  magnet  frame  (see  §  60), 
but  which  may  also  be  made  use  of  in  obtaining  an  approxi- 
mate value  of  the  leakage  coefficient  for  rough  calculations. 

From  said  table  the  general  rule  will  be  noted  that  the  factor 
of  leakage  is  the  greater  the  smaller  the  dynamo,  which  is  due 
to  the  difficulty,  or  rather  impossibility,  of  properly  dimension- 
ing the  magnetic  circuit  in  small  machines.  In  these  the  length 
of  the  air  gaps  is  comparatively  much  larger,  and  the  relative 


1  For  list  of  machines  considered  see  Preface. 

2  J.  and  E.  Hopkinson,  Phil.  Trans.,  1886,  part  i. 

3  Lahmeyer,  Elektrotechn.  Zeitschr.,  vol.  ix.  pp.  89  and  283  (1888). 
4 Corsepius,  Elektrotechn.  Zeitschr.,  vol.  ix.  p.  235  (1888). 

5  W.  B.  Esson,  The  Electrician  (London),  vol.  xxiv.  p.  424  (1890);  Journal 
Inst.  El.  Eng.,  vol.  xix.  p.  122  (1890). 

'  W.  Wedding,  Elektrotechn.  Zeitschr.,  vol.  xiii.  p.  67  (1892). 

7  Arthur  Stanley  Ives,  Electrical  World,  vol.  xix.  p.  u  (January  2,  1892). 

s  Edwin  Edser  and  Herbert  Stansfield,  Electrical  World,  vol.  xx.  p.  180 
(September  17,  1892). 

9  Puffer,  Electrical  Review  (London),  vol.  xxx.  p.  487  (1892). 


§  7O]     CALCULA  TIO^T  OF  A  CTUAL  MA  GNE  TIC  LEA KA  GE.      2 63 


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264  DYNAMO-ELECTRIC  MACHINES.  [§  7O 

distances  of  the  leakage  surfaces  much  smaller  than  in  large 
dynamos ;  the  permeance  of  the  air  gaps,  therefore,  is  relatively 
much  smaller,  while  the  permeances  of  the  leakage  paths  are 
considerably  larger,  comparatively,  than  in  large  machines, 
and  formula  (157),  in  consequence,  will  produce  a  high  value 
of  the  leakage  coefficient  for  a  small  dynamo. 

It  further  follows  from  Table  LXVIII.  that  the  leakage  factor 
for  various  types  and  sizes  of  dynamos  varies  within  the  wide 
range  of  from  i.io  to  2.00,  which  result  agrees  with  observa- 
tions of  Mavor,1  who,  however,  seems  not  to  have  considered 
capacities  over  100  KW. 

By  comparing  the  values  of  A  for  any  one  capacity,  the  rela- 
tive merits  of  the  various  types  considered  may  be  deduced. 

Thus  it  is  learned  that,  as  far  as  magnetic  leakage  is  con- 
cerned, the  Horizontal  Double  Magnet  Type  (column  6)  and 
the  Bipolar  Iron -clad  Type  (column  7)  are  superior  to  any  of 
the  other  types,  which  undoubtedly  is  due  to  the  common 
feature  of  these  types  of  having  the  cores  of  opposite  magnetic 
potential  in  line  with  each  other  on  opposite  sides  of  the  arma- 
ture, thus  reducing  the  magnetic  leakage  between  them  to  a 
minimum. 

Next  in  line,  considering  bipolar  dynamos,  are  the  Inverted 
Horseshoe  Type  (column  2),  the  Single  Magnet  Type  (column 
4),  the  Upright  Horseshoe  Type  (column  i),  and  the  Vertical 
Double  Horseshoe  Type  (column  8). 

Of  multipolar  machines  the  two  best  forms,  magnetically,  are, 
respectively,  the  Innerpole  Type  (column  13),  and  the  Radial 
Multipolar  Type  (column  12).  In  the  first  named  of  these 
types  the  magnet  cores  form  a  star,  having  a  common  yoke  in 
the  centre  and  the  polepieces  at  the  periphery;  thus  the  dis- 
tances of  the  leakage  paths  increase  the  direct  proportion  to 
the  difference  of  magnetic  potential,  a  feature  which  is  most 
desirable,  and  which  accounts  for  the  low  values  of  A  for  the 
type  in  question. 

The  most  leaky  of  all  types  seem  to  be  the  Horizontal  Single 
Horseshoe  Type  (column  3),  and  the  Axial  Multipolar  Type 
(column  15). 


1  Mavor,  Electrical  Engineer  (London),  April  13,   1894  ;  Electrical  World \ 
vol.  xxiii.  p.  615,  May  5,  1894. 


§  70]     CALCULA  TION  OF  ACTUAL  MA  GNE  TIC  LEAK  A  GE.      265 

In  the  former  type  the  excessive  leakage  is  due  to  the  mag- 
netic circuit  being  suspended  over  an  iron  surface  extending 
over  its  entire  length,  while  in  the  latter  type  it  is  due  to  the 
comparatively  close  relative  proximity  of  a  great  number  of 
magnet  cores  (two  for  each  pole)  parallel  to  each  other. 


PART  IV. 


DIMENSIONING  OF  FIELD  MAGNET  FRAME. 


CHAPTER  XIV. 

FORMS    OF    FIELD    MAGNETS. 

71.  Classification  of  Field  Magnet  Frames. 

With  reference  to  the  type  of  the  field  magnet  frame  mod- 
ern dynamos  may  be  classified  as  follows : 

/. — Bipolar  Machines. 

1.  Single  Horseshoe  Type. 

a.  Upright  single  horseshoe  type  (Fig.  187). 

b.  Inverted  single  horseshoe  type  (Fig.  188). 

c.  Horizontal  single  horseshoe  type  (Fig.  189). 

d.  Vertical  single  horseshoe  type  (Fig.  190). 

2.  Single  Magnet  Type. 

a.  Horizontal  single  magnet  type  (Figs.  191  and  192). 

b.  Vertical  single  magnet  type  (Fig.  193). 

c.  Single  magnet  ring  type  (Fig.  194). 

3.  Double  Magnet  Type. 

a.  Horizontal  double  magnet  type  (Figs.  195  and  197). 

b.  Vertical  double  magnet  type  (Figs.  196  and  199). 

c.  Inclined  double  magnet  type  (Fig.  198). 
*     d.   Double  magnet  ring  type  (Fig.  200). 

4.  Double  Horseshoe  Type. 

a.  Horizontal  double  horseshoe  type  (Fig.  201). 

b.  Vertical  double  horseshoe  type  (Fig.  202). 

5.  Iron-clad  Type. 

a.  Horizontal  iron-clad  type  (Figs.  203  and  204). 

b.  Vertical  iron-clad  type. 

a.  Single  magnet  vertical  iron-clad  type  (Figs.  205  and 

206). 
/3.   Double  magnet  vertical  iron-clad  type  (Fig.  207). 

//.  — Multipolar  Machines. 
i.   Radial  Multipolar  Type. 

a.  Radial  outerpole  type  (Fig.  208). 

b.  Radial  innerpole  type  (Fig.  209). 

-     269 


270  DYNAMO-ELECTRIC  MACHINES.  [§72 

2.  Tangential  Multipolar  Type. 

a.  Tangential  outerpole  type  (Fig.  210). 

b.  Tangential  innerpole  type  (Fig.  211). 

3.  Axial  Multipolar  Type  (Fig.  212). 

4.  Radi-tangent  Multipolar  Type  (Fig.  213). 

5.  Single  Magnet  Multipolar  Type. 

a.  Axial  pole  single  magnet  multipolar  type  (Fig.  214). 

b.  Outer-innerpole    single  magnet   multipolar  type  (Fig. 

2I5)- 

6.  Double  Magnet  Multipolar  Type  (Fig.  216). 

7.  Multipolar  Iron-clad  Type  (Fig.  217). 

Horizontal   fourpolar  iron-clad   type   (Figs.    218  and 

220). 
Vertical  fourpolar  iron-clad  type  (Fig.  219). 

8.  Multiple  Horseshoe  Type  (Figs.  221  and  222). 

9.  Fourpolar  Double  Magnet  Type  (Fig.  223). 
10.   Quadruple  Magnet  Type  (Fig.  224). 

72.  Bipolar  Types. 

The  simplest  form  of  field  magnet  frame  is  that  resembling 
the  shape  of  a  horseshoe.  Such  a  horseshoe-shaped  frame 
may  be  composed  of  two  magnet  cores  joined  by  a  yoke,  or 
may  be  formed  of  but  one  electromagnet  provided  with  suit- 
ably shaped  polepieces.  The  former  is  called  the  single  horse- 
shoe type,  the  latter  the  single  magnet  type. 

A  single  horseshoe  frame  may  be  placed  in  four  different  po'si- 
tions  with  reference  to  the  armature,  the  two  cores  either 
being  above  or  below  the  armature,  or  situated  symmetrically. 
one  on  each  side,  in  a  horizontal  or  in  a  vertical  position. 

The  upright  single  horseshoe  type,  Fig.  187,  is  the  realization  of 
the  first  named  arrangement,  having  the  armature  below  the 
cores,  and  is  therefore  often  called  the  "  undertype"  This 
form  is  now  used  in  the  Edison  dynamo,1  built  by  the  General 
Electric  Co.,  Schenectady,  N.  Y.,  in  the  motors  of  the  "C  & 
C"  (Curtis  &  Crocker)  Electric  Co.,2  New  York,  and  is  fur- 
ther employed  by  the  Adams  Electric  Co.,  Worcester,  Mass.; 


1  Electrical  Engineer,  vol.  xiii.  p.  391  (1891);   Electrical  World,  vol.  xix.  p. 
220  (1892). 

2  Martin  and  Wetzler,  "  The  Electric  Motor,"  third  edition,  p.  230. 


§72] 


FORMS  OF  FIELD   MAGNETS. 


271 


by  the  £.  G.  Bernard  Company,  Troy,  N.  Y. ;    by  the  Detroit 
Electrical  Works,1  Detroit,  Mich.  ("King"  dynamo);  the  Com-_ 


FIG.  205  FlQ.  206  FIG.  207 

Figs.  187  to  207. — Types  of  Bipolar  Fields. 

mercial  Electric  Co.2  (A.  D.  Adams),   Indianapolis,  Ind. ;    the 
Novelty  Electric  Co.,3  Philadelphia,  Pa.;   the  Elektron  Manu- 


1  Electrical  World,  vol.  xxi.  p.  165  (1893). 

2  Electrical  World,  vol.  xx.  p.  430  (1892). 

3  Electrical  World,  vol.  xvi.  p.  404  (1890). 


272  D  YNAMO-ELECTRIC  MA  CHINES.  [§  72 

facturing  Co.1  (Ferret),  Springfield,  Mass.;  by  Siemens 
Bros.,2  London,  Eng. ;  Mather  &  Platt 3  (Hopkinson),  Man- 
chester, Eng.  ;  the  India-rubber,  Guttapercha  and  Telegraph 
Works  Co.,4  Silvertown,  Eng.,  and  by  Clarke,  Muirhead  & 
Co.,  London. 

The  inverted  horseshoe  type,  Fig.  188,  having  the  armature 
above  the  cores,  is  also  called  the  "overtype"  Of  this  form 
are  the  General  Electric  Co. 's  "  Thomson-Houston  Motors," 
the  standard  motors  of  the  Crocker-Wheeler  Electric  Co.,5 
Ampere,  N.  J.;  further,  machines  of  the  Keystone  Electric 
Co.,6  Erie,  Pa.;  the  Belknap  Motor  Co.,7  Portland,  Me.;  the 
Holtzer-Cabot  Electric  Co.,6  Boston,  Mass.;  the  Card  Electric 
Motor  and  Dynamo  Co.,9  Cincinnati,  O. ;  the  La  Roche  Elec- 
trical Works,10  Philadelphia,  Pa. ;  the  Excelsior  Electric  Co.,11 
New  York;  the  Zucker  &  Levett  Chemical  Co.,13  New  York 
(American  "  Giant"  dynamo);  the  Knapp  Electric  and  Nov- 
elty Co.,13  New  York;  the  Aurora  Electric  Co.,14  Philadelphia, 
Pa.;  the  Detroit  Motor  Co.,16  Detroit,  Mich.;  the  National 
Electric  Manufacturing  Co.,16  Eau  Claire,  Wis. ;  Patterson  & 

1  Electrical  Engineer,  vol.  xiii.  p.  8  (1892). 

2  Silv.  P.  Thompson,  "  Dynamo-Electric  Machinery,"  fourth  edition,  p.  509. 

3  Silv.  P.  Thompson,  "  Dynamo-Electric  Machinery,"  fourth  edition,  pp.  519 
and  522. 

4  Electrical  World,  vol.  xiii.  p.  84  (1889). 

5  Electrical  World,  vol.  xvii.  p.  130  (1891);    Electrical  Engineer,  vol.  xiv.  p. 
199  (1892). 

6  Electrical  World,  vol.  xix.  p.  220  (1892). 

^Electrical  World,  vol.  xxi.  p.  470  (1893);  Electrical  Engineer,  vol.  xiv.  p. 
210  (1892). 

8  Electrical  Engineer,  vol.  xvii.  p.  291  (1894). 

9  Electrical  World,  vol.  xxiii;  p.  499  (1894);   Electrical  Engineer,  vol.  xi.  p. 
13  (1891).    (This  company  is  now  the  Bullock  Electric  Manufacturing  Company.) 

10  Electrical  World,  vol.  xvii.  p.  17  (1893);  Electrical  Engineer,  vol.  xiv.  p. 
559  (1892);  vol.  xv.  p.  491  (1893). 

11  Electrical  Engineer,  vol.  xiv.  p.  240  (1892). 

12  Electrical  Engineer,  vol.  xiv.  p.  187  (1892);  Electrical  World,  vol.  xxii.  p. 
210  (1893).     (Now  the  Zucker,  Levett  &  Loeb  Company.) 

13  Electrical  World,  vol.  xxi.  pp.  286,  306,  471  (1893). 

14  Electrical  World,  vol.  xv.  p.  II  (1890). 

15  Electrical   World,  vol.  xvi.  p.  437  (1890);   Electrical  Engineer,  vol.  x.  p. 
<695  (1890). 

16  Electrical   World,  vol.  xvi.  pp.  121,  419  (1890);   vol.  xxiv.  p.   22O  (1894); 
Electrical  Engineer,  vol.  xviii.  p.  178  (1894). 


§72]  FORMS  OF  FIELD  MAGNETS.  273 

Cooper1  (Esson),  London;  Johnson  &  Phillips2  (Kapp),  Lon- 
don; Siemens  &  Halske,3  Berlin,  Germany;  Ganz  &  Co.,4 
Budapest,  Austria  ;  Allgemeine  Elektricitats  Gesellschalt,6 
Berlin;  Berliner.  Maschinenbau  Actien-gesellschaft,  vorm.  L. 
Schwartzkopff,6  Berlin;  and  Zuricher  Telephon  Gesellschaft,7 
Zurich,  Switzerland. 

Machines  of  the  horizontal  single  horseshoe  type,  Fig.  189,  in 
which  the  centre  lines  of  the  two  magnet  cores  and  the  axis  of 
the  armature  lie  in  the  same  horizontal  plane,  are  built  by  the 
Jenney  Electric  Co.,8  New  Bedford,  Mass.  ("Star"  dynamo), 
by  the  Great  Western  Manufacturing  Co.9  (Bain),  Chicago, 
111.,  and  by  O.  L.  Kummer  &  Co.,10  Dresden,  Germany. 

The  vertical  single  horseshoe  type,  Fig.  190,  finally,  having  the 
axes  of  magnet  cores  and  armature  in  one  vertical  plane,  is 
employed  by  the  Excelsior  Electric  Co.11  (Hochhausen),  New 
York,  and  by  the  Donaldson-Macrae  Electric  Co.,12  Baltimore, 
Md. 

Single  core  hosseshoe  frames  may  be  designed  by  placing  the 
magnet  either  in  a  horizontal  or  in  a  vertical  position,  or  by 
joining  two  polepieces  of  suitable  shape  by  a  magnet  of  circu- 
lar form.  The  types  thus  obtained  are  the  horizontal  single 
magnet  type,  the  vertical  single  magnet  type,  and  the  single  magnet 
ring  type. 

In  the  horizontal  single  magnet  type,  Figs.  191  and  192  respect- 
ively, the  armature  may  either  be  situated  above  or  below  the 
core.  Machines  of  the  former  type  (Fig.  191)  are  built  by  the 

I  S.  P.  Thompson,  "  Dynamo-Electric  Machinery,"  plate  v. 

2S.  P.  Thompson,  "  Dynamo-Electric  Machinery,"  plates  i  and  ii. 

3  Elektrotechn.  Zeitschr.,  vol.  vii.  p.  13  (1886);   Kittler,    "  Handbuch,"  vol. 
i.p.  851. 

4  Zeitschr.  f.  Electroteckn.,  vol.  vii,  p.  78  (1889);  Kittler,  "  Handbuch,"  vol. 
i.  p.  930. 

5Grawinkel  and  Strecker,  "  Hilfsbuch,"  fourth  edition  (1895),  p.  287. 
6Grawinkel  and  Strecker,  "  Hilfsbuch,"  fourth  edition,  p.  288. 

7  Grawinkel  and  Strieker,  "  Hilfsbuch,"  fourth  edition,  p.  328. 

8  Electrical  World,  vol.  xix.  p.  172  (1892);   Electrical  Engineer,  vol.  xiii.  p. 
182  (1892). 

9  Electrical  Engineer,  vol.  xvii.   p.  421  (1894).     (Now   the   Western    Elec- 
tric Co. ) 

10  Kittler,  "  Handbuch,"  vol.  i.  p.  949. 

II  Electrical  Engineer,  vol.  xvii.  p.  465  (1894). 
12  Electrical  Engineer,  vol.  xiii.  p.  397  (1892). 


274  D  YNA MO- EL  EC  TRIG  MA  CHINES.  [§  7  2 

Jenney  Electric  Motor  Co.,1  Indianapolis,  Ind. ;  the  Porter 
Standard  Motor  Co.,  New  York;  the  Fort  Wayne  Electric 
Corp.,2  Fort  Wayne,  Ind. ;  the  United  States  Electric  Co.,  New 
York;  the  Holtzer-Cabot  Electric  Co.,3  Boston;  the  Card 
Electric  Motor  and  Dynamo  Co.,4  Cincinnati,  O. ;  the  Simp- 
son Electrical  Manufacturing  Co.,5  Chicago;  the  Chicago 
Electric  Motor  Co.,6  Chicago;  the  Bernstein  Electric  Co.,7 
Boston;  and  by  the  Premier  Electric  Co.,8  Brooklyn.  The 
latter  type,  Fig.  192,  is  employed  by  the  Elektron  Manufac- 
turing Co.,9  Springfield,  Mass.;  by  the  Riker  Electric  Motor 
Co.,10  Brooklyn;  and  by  the  Actiengesellschaft  Elektricitat- 
werke,  vorm.  O.  L.  Kummer  &  Co.,11  Dresden. 

The  vertical  single  magnet  type,  Fig.  193,  is  used  by  the 
"D.  &  D."  Electric  Manufacturing  Company,12  Minneapolis, 
Minn. ;  the  Packard  Electric  Company,18  Warren,  O. ;  the  Bos- 
ton Motor  Company,14  Boston;  the  Elbridge  Electric  Man- 
ufacturing Company,  Elbridge,  N.  Y. ;  the  Woodside  Electric 
Works  1B(Rankin  Kennedy),  Glasgow,  Scotland;  by  Greenwood 
&  Batley,1'  Leeds,  England ;  by  Goolden  &  Trotter17  (Atkinson), 
England;  and  by  Naglo  Bros.,18  Berlin. 


1  Electrical  Engineer ',  vol.  xiii.  p.  182  (1892.) 

2  Electrical  Engineer,  vol.  xiii.  p.  408  (1892);   Electrical  World,   vol.  xxviii. 
p.  394  (1896). 

3  Electrical  World,  vol.  xix.  p.  107  (1892). 

4  Electrical  World,  vol.  xxiii.  p.  499  (1894). 

5  Electrical  World,  vol.  xxii.  p.  30  (1893). 

6  Electrical  World,  vol.  xxii.  p.  31  (1893). 

7  Electrical  World,  vol.  xix.  p.  283  (1892). 

8  Electrical  World,  vol.  xix.  p.  186  (1892). 

9  Electrical  Engineer,  vol.  xv.  p.  540(1893). 
10 Electrical  Engineer •,  vol.  xvi.  p.  436  (1893). 

11  Grawinkel  and  Strecker,  "  Hilfsbuch,"  fourth  edition,  p.  277. 

12  Electrical  World,  vol.  xx.  p.  183  (1892);  Electrical  Engineer,  vol.  xiv.   p. 
272  (1892). 

13  Electrical  World,  vol.  xx.  p.  265.  (1892),  Electrical  Engineer,  vol.  xiv.    p. 
414(1892). 

^Electrical  World,  vol.  xxi.  p.  471  (1893). 

15  7 'he  Electrician  (London),  March   I,    1889;  Electrical  World,   vol.   xiii., 
April,  1889. 

16  Silv.  P.  Thompson,  "  Dynamo-Electric  Machinery,"  fourth  edition,  p.  531. 
"Silv.  P.  Thompson,  "  Dynamo-Electric  Machinery,"  fourth  edition,  p.  615. 
18  Grawinkel  and  Strecker,  "  Hilfsbuch,"  fourth  edition,  p.  314. 


g  72]  FORMS  OF  FIELD  MAGNETS.  275 

Fig.  194  shows  the  single  magnet  ring  type,  which  is  employed 
by  the  Mather  Electric  Company,1  Manchester,  Conn. 

Two  magnets,  instead  of  forming  the  limbs  of  a  horseshoe, 
can  also  be  set  in  line  with  each  other,  one  on  each  side  of  the 
armature,  or  may  be  arranged  so  as  to  be  symmetrical  to  the 
armature,  but  with  like  poles  pointing  to  the  same  direction, 
instead  of  forming  a  single  magnetic  circuit  with  salient  poles; 
the  frame  will  then  constitute  a  double  circuit  with  consequent 
poles  in  the  yokes  joining  the  respective  ends  of  the  magnet 
cores.  In  both  of  these  cases  the  cores  may  be  put  in  a  hori- 
zontal or  vertical  position,  and  in  consequence  we  obtain  two 
horizontal  double  magnet  types,  Figs.  195  and  197,  and  two  vertical 
double  magnet  types,  Figs.  196  and  199. 

The  salient  pole  horizontal  double  magnet  type,  Fig.  195,  is  em- 
ployed by  Naglo  Bros.,2  Berlin,  and  by  Fein  &  Company,  Stutt- 
gart, Germany ;  and  the  salient  pole  vertical  double  magnet  type, 
Fig.  196,  by  the  Edison  Manufacturing  Company,3  New  York; 
and  by  Siemens  &  Halske,4  Berlin. 

The  consequent  pole  horizontal  double  magnet  type,  Fig.  197,  is 
used  in  the  Feldka"mp  motor,  built  by  the  Electrical  Piano 
Company,5  Newark,  N.  J. ;  and  in  the  fan  motor  of  the  De 
Mott  Motor  and  Battery  Company;6  and  the  consequent  pole 
vertical  double  magnet  type,  Fig.  199,  by  the  Columbia  Electric 
Company,7  Worcester,  Mass. ;  the  Keystone  Electric  Company, 
Erie,  Pa. ;  the  Akron  Electrical  Manufacturing  Company,8 
Akron,  O. ;  the  Mather  Electric  Company,9  Manchester, 
Conn. ;  the  Duplex  Electric  Company,10  Corry,  Pa. ;  the  Gen- 


1  Electrical  Engineer,  vol.  xvii.  p.  181  (1894). 

3  Kittler,  "  Handbuch,"  vol.  i.  p.  908;  Jos.  Kramer,  "  Berechnung  der  Dy- 
namo Gleichstrom  Maschinen." 

3  "  Composite"  Fan  Motor,  Electrical Engineer ',  vol.  xiv.  p.  140(1893)  ;  Elec- 
trical World,  vol.  xxviii.  p.  375  (1896);  Electrical  Age,  vol.  xix.  p.  269  (1897). 

4  Grawinkel  and  Strecker,  "  Hilfsbuch,"  fourth  edition,  p.  326. 
^Electrical  World,  vol.  xxi.  p.  240  (1893). 

6  Electrical  World,  vol.  xxi.  p.  395  (1893). 

7  Electrical  World,  vol.  xxiii.  p.  849(1894). 

8  Electrical  World,  vol.  xx.  p.  264  (1892). 

9  Electrical  World,  vol.  xxiv.  p.  112  (1894);  Electrical  Engineer,  vol.  xviii. 
p.  99  (1894). 

10  Electrical  World,  vol.  xix.  pp.  107,  171   (1892);  Electrical  Engineer,   vol. 
xiii.  p.  198(1892). 


276  DYNAMO-ELECTRIC  MACHINES.  [§72 

eral  Electric  Traction  Company  (Snell),  England;  Mather  & 
Platt  (Hopkinson),1  Manchester,  England;  Immish  &  Com- 
pany,2 England;  Oerlikon  Works  (Brown),3  Zurich,  Switzer- 
land; Helios  Company,4  Cologne;  and  by  Naglo  Bros.,e  Berlin. 

If  in  the  latter  form  the  magnets  are  made  of  circular  shape, 
the  double  magnet  ring  type.  Fig.  200,  is  obtained,  which  is  built 
by  the  "C  &  C"  Electric  Company,6  New  York,  and  which 
has  been  used  in  the  Griscom  motor7  of  the  Electro-dynamic 
Company,  Philadelphia. 

The  inclined  double  magnet  type,  illustrated  in  Fig.  198,  forms 
the  connecting  link  between  the  double  magnet  and  the  single 
horseshoe  types;  it  is  employed  by  the  Baxter  Electrical  Manu- 
facturing Company,8  Baltimore,  Md. ;  by  Fein  &  Company,9 
Stuttgart;  and  by  Schorch  10  in  Darmstadt. 

The  combination  of  two  horseshoes  with  common  polepieces 
furnishes  two  further  forms  of  field  magnet  frames.  Fig.  201 
shows  the  horizontal  double  horseshoe  type,  and  Fig.  202  the  ver- 
tical double  horseshoe  type. 

Machines  of  the  former  type  (Fig.  201)  are  built  by  the 
United  States  Electric  Company "  (Weston),  New  York;  the 
Brush  Electric  Company,12  Cleveland,  O. ;  the  Ford-Washburn 
Storelectric  Company,  Cleveland,  O. ;  the  Western  Electric 
Company,13  Chicago,  111.;  the  Fontaine  Crossing  and  Electric 
Company  (Fuller),  Detroit,  Mich, ;  by  Crompton  &  Com- 
pany,14 London,  England;  by  Lawrence,  Paris  &  Scott,  Eng- 
land, and  by  Schuckert  &  Company,  Nuremberg,  Germany. 

The  latter  form  (Fig.  202)  is  employed  in  dynamos  of  Fort 


1  Silv.  P.  Thompson,  "  Dynamo-Electric  Machinery,"  fourth  edition,  p.  496. 

2  Gisbert  Kapp,  "  Transmission  of  Energy,"  p.  272. 

3  Kittler,  "  Handbuch,"  vol.  i.  p.  921. 
4Kittler,  "  Handbuch,"  vol.  i.  p.  904. 

5Grawinkel  and  Strecker,  "  Hilfsbuch,"  fourth  edition,  p.  312. 

6  Electrical  World,  vol.  xxii.  p.  247  (1892). 

7  Martin  and  Wetzler,  "  The  Electric  Motor,"  third  edition,  p.  126. 
9  Martin  and  Wetzler,  "  The  Electric,  Motor,"  third  edition,  p.  228. 

9  Kittler,  "  Handbuch,"  vol.  i.  p.  944. 

10  Jos.  Kramer,  "  Berechnung  der  Gleichstrom  Dynamo  Maschinen." 

11  Kittler,  "  Handbuch,"  vol.  i.  p.  879. 

12  Electrical  Engineer,  vol.  xiv.  p.  50  (1892). 

13  Electrical  Engineer,  vol.  xvi.  p.  323  (1893). 
34  Kapp,  "  Transmission  of  Energy,"  p.  292. 


§  72]  FORMS  OF  FIELD  MAGNETS.  277 

Wayne  Electric  Corporation l  (Wood),  Fort  Wayne,  Ind. ; 
La  Roche  Electric  Works,2  Philadelphia;  Granite  State  Electric 
Company,3  Concord,  N.  H. ;  Onondaga  Dynamo  Company, 
Syracuse,  N.  Y. ;  Electric  Construction  Corporation4  (Elwell- 
Parker);  and  Crompton  Company,6  London,  England. 

If  one  or  both  the  polepieces  of  a  consequent  pole  double 
magnet  type  are  prolonged  in  the  axial  direction,  that  is,  to- 
ward the  armature,  and  the  winding  is  transferred  from  the 
cores  to  these  elongated  polepieces,  then  a  type  is  obtained  in 
which  the  magnet  frame  forms  a  closed  iron  wrappage  with  in- 
wardly protruding  poles.  Forms  of  this  feature  are  known  as 
iron-clad  types,  and,  according  to  the  number  of  magnets  and  to 
their  position,  are  single  magnet  and  double  magnet,  horizontal 
and  vertical  iron-clad  types. 

Fig.  203  shows  the  horizontal  iron-clad  type,  having  two  hori- 
zontal magnets.  It  is  used  by  the  General  Electric  Com- 
pany,6 Schenectady,  N.Y.  (Thomson-Houston  Arc  Light  type), 
Detroit  Electric  Works,7  Detroit,  Mich. ;  Eickemeyer  Com- 
pany,8 Yonkers,  N.  Y. ;  Fein  &  Company,9  Stuttgart;  and 
Aachen  Electrical  Works  10  (Lahmeyer),  Aachen,  Germany. 

A  modification  of  this  type  consists  in  letting  the  poles  pro- 
ject parallel  to  the  shaft,  one  above  and  one  below,  or  one  on 
each  side  of  the  armature;  the  only  magnetizing  coil  required 
in  this  case  will  completely  surround  the  armature.  This  spe- 
cial horizontal  iron-clad  form,  which  is  illustrated  in  Fig.  204, 
is  realized  in  the  Lundell  machine,11  built  by  the  Interior  Con- 
duit and  Insulation  Company,  New  York. 

1  Electrical  World,  vol.  xxiii.  p.  845  (1894);  v°l-  xxviii.  p.  390  (1896);  Elec- 
trical Engineer,  vol.  xvii.  p.  598  (1894). 

2  Electrical  Engineer,  vol.  xiii.  p.  439  (1892). 
^  Electrical  Engineer,  vol.  xvi.  p.  45  (1893). 

4  Electrical  Engineer,  vol.  xv.  p.  166  (1893). 

5  Silv.  P.  Thompson,  "  Dynamo-Electric  Machinery,"  fourth  edition,  p.  486. 
•Silv.  P.  Thompson,  "  Dynamo-Electric  Machinery,"  fourth  edition,  p.  465. 

7  Electrical  World,  vol.  xx.  p.  46  (1892)  ;    Electrical  Engineer,   vol.    xiv. 
p.  27(1892). 

8  Kittler,  "  Handbuch,"  vol.  i.  p.  941. 
9Kittler,  "  Handbuch,"  vol.  i.  p.  944. 

10  Kittler,  "  Handbuch,."  vol.  i.  p.  917. 

11  Electrical    World,  vol.    xx.   pp.    13,    381   (1892);  vol.  xxiii.  p.  32   (1894); 
Electrical  Engineer,  vol.  xiii.  p.  643  (1892);  vol.  xiv.  p.  544(1892);  vol.  xvii.  p, 
17  (1894.) 


278  DYNAMO-ELECTRIC  MACHINES.  [§72 

In  Figs.  205  and  206  the  two  possible  cases  of  the  vertical  single 
magnet  iron-clad  type  are  depicted,  the  magnet  being  placed 
above  the  armature  in  the  former  and  below  the  armature  in  the 
latter  case.  The  single  magnet  iron-clad  overtype,  Fig.  205,  is 
adopted  in  the  street-car  motors  of  the  General  Electric  Com- 
pany, Schenectady,  N.  Y. ;  in  the  machines  of  the  Muncie 
Electrical  Works,1  Muncie,  Ind. ;  of  the  Lafayette  Engineering 
and  Electric  Works,2  Lafayette,  Ind.,  arid  in  the  battery  fan 
motor  of  the  Edison  Manufacturing  Company,3  New  York. 
Machines  of  the  single  magnet  iron-clad  undertype,  Fig.  206,  are 
built  by  the  Brush  Electrical  Engineering  Company 4  (Mor- 
dey),  London,  and  by  Stafford  and  Eaves,5  England. 

The  vertical  double  magnet  iron-clad  type,  Fig.  207,  having  two 
vertically  projecting  magnets,  one  above  and  one  below  the 
armature,  is  employed  in  the  machines  of  the  Wenstrom  Elec- 
tric Company,6  Baltimore;  the  Triumph  Electric  Company,7 
Cincinnati,  O.  ;  the  Shawhan-Thresher  Electric  Company,8 
Dayton,  O. ;  the  Card  Motor  Company,9  Cincinnati,  O.  ;  the 
Johnson  Electric  Service  Company,10  Milwaukee,  Wis. ;  the 
Erie  Machinery  Supply  Company,11  Erie,  Pa.;  O.  L.  Kummer 
&  Company,12  Dresden  ;  Deutsche  Elektrizitats-Werke18 
(Garbe,  Lahmeyer  &  Co.),  Aachen;  Schuckert  &  Company,14 
Nuremburg,  Germany;  Oerlikon  Works,15  Zurich;  and  the 
Zurich  Telephone  Company,16  Zurich,  Switzerland. 

There   are   various    other    bipolar   types,    which,    however, 


^Electrical  Engineer,  vol.  xv.  p.  606  (1893). 

2  Western  Electrician,  vol.  xviii.  p.  273  (1896). 

3  Electrical  World,  vol.  xxi.  p.  347  (1893). 

4  Elektrotechn.  Zeitschr.,  vol.  xi.  p.  135  (1890). 

6  S.  P.  Thompson,  "  Dynamo-Electric  Machinery,"  fourth  edition,  p.  202. 
6  Elektrotechn.  Zeitschr.,  vol.  xi.  p.  122  (1890). 

I  Electrical  Engineer,  vol.  xvii.  p.  314  (1894). 
s  Electrical  World,  vol.  xxiii.  p.  191  (1894). 

9  Electrical  World,  vol.  xxii.  p.  15  (1893). 

10  Electrical  Engineer,  vol.  xvii.  p.  290(1894). 

II  Electrical  World,  vol.  xix.  p.  283  (1892). 

12Grawinkel  and  Strecker,  "  Hilfsbuch,"  fourth  edition,  p.  278. 
13Grawinkel  and  Strecker,  "  Hilfsbuch,"  fourth  edition,  p.  293. 

14  Grawinkel  and  Strecker,  "  Hilfsbuch,"  fourth  edition,  p.  299. 

15  Grawinkel  and  Strecker,  "  Hilfsbuch,"  fourth  edition,  p.  320. 

16  Elektrotechn.  Zeitschr.,  vol.  ix.  pp.  181,  347,  410  and  485  (1888). 


§73] 


FORMS   OF  FIELD  MAGNETS. 


279 


mostly  are  out  of  date,  and,  therefore,  of  very  little  practical 
importance.  These  can  easily  be  regarded  as  special  cases  of 
the  types  enumerated  above. 

73.  Multipolar  Types. 

Multipolar  field   magnet   frames  can  have  one  or  two   mag- 
nets for  every  pole,  or  each  magnet  can  independently  supply 


Fia.212. 


FIG.  .21 7 


FIG.  21 3  FIG.  21 4  FIG.  215         FIG.  21 6 


FIG.  21 8 


FIG.  21 9 


FIG.  220 


FIG.  222  FIG.  223  FIG.  224 

Figs.  208  to  224. — Types  of  Multipolar  Fields. 

two  poles,  or  one  single  magnet,  or  two  magnets,  may  be  pro- 
vided with  polepieces  of  such  shape  as  to  form  the  desired 
number  of  poles  of  opposite  polarity. 


280  DYNAMO-ELECTRIC  MACHINES.  [§73 

If  the  number  of  magnets  is  identical  with  the  number  of 
poles,  the  magnets  may  either  be  placed  in  a  radial,  a  tangetial, 
or  an  axial  position  with  reference  to  the  armature,  and  in  the 
two  first-named  cases  they  may  be  put  either  outside  or  inside  of 
the  armature. 

The  Radial  Outerpole  Type  is  shown  in  Fig.  208;  this  form 
has  been  adopted  as  the  standard  type  for  large  dynamos  of 
the  General  Electric  Company,1  Schenectady,  N.  Y. ;  of  the 
Westinghouse  Electric  and  Manufacturing  Company,2  Pitts- 
burg,  Pa.;  the  Crocker-Wheeler  Electric  Company,3  Ampere, 
N.  J. ;  the  Riker  Electric  Motor  Company,4  Brooklyn;  the 
Stanley  Electric  Manufacturing  Company,5  Pittsfield,  Mass.; 
the  Fort  Wayne  Electric  Company,6  Fort  Wayne,  Ind. ;  the 
Eddy  Electric  Manufacturing  Company,7  Windsor,  Conn.;  the 
Belknap  Motor  Company,8  Portland,  Me.;  the  Shawhan- 
Thresher  Electric  Company,9  Dayton,  O. ;  the  Great  Western 
Electric  Company10  (Bain),  Chicago;  the  Walker  Manufactur- 
ing Company,11  Cleveland,  O. ;  the  Mather 'Electric  Com- 
pany,12 Manchester,  Conn.;  the  Claus  Electric  Company,13 
New  York;  the  Commercial  Electric  Company,14  Indianapolis; 


1  Electrical  World,  vol.  xxi.  p.  335  (1893);  vol.  xxiv.  pp.  557  and  652  (1894); 
Electrical  Engineer,   vol.    xiii.    p.  165  (1892) ;  vol.   xiv.    p.    562   (1892);  vol. 
xviii.  pp.  426,  507  (1894). 

2  Electrical  World,  vol.  xxi.  p.  91  (1893);  vol.  xxiv.  p.  421  (1894);  Electrical 
Engineer,  vol.  xviii.  p.  330  (1894). 

3  Electrical  World,  vol.  xxiii.    p.   307  (1894);  Electrical  Engineer,  vol.  xvii. 
p.  193  (1894). 

4  Electrical  World,  vol.  xxiii.  p.  687  (1894);  Electrical  Engineer,  vol.  xvii.  p. 
442  (1894). 

5  Electrical  World,  vol.  xxiii.  p.  815  (1894);  Electrical  Engineer,  vol.  xvii.  p. 
507  (1894). 

6  Electrical  World,  vol.  xxiii.  p.  878  (1894);  vol.  xxviii.  p.  395  (1896). 

7  Electrical  World,  vol.  xxv.  p.  34  (1895). 

8  Electrical  Engineer,  vol.  xvii.  p.  502  (1894). 

9  Electrical  Engineer ,  vol.  xvii.  p.  463  (1894). 

10  Electrical  World,  vol.  xxiii.  p.  161  (1894). 

11  Electrical  World,  vol.  xxiii.  pp.  475    and   785    (1894);    vol.    xxviii.  p.  423 
(1896);  Electrical  Age,  vol.  xviii.  p.  605  (1896). 

12  Electrical  Engineer,  vol.  xiv.  p.  364  (1892). 

13  Electrical  Engineer,  vol.  xvi.  p.  3  (1893). 

14 Electrical  World,  vol.  xxiv.  p.  627  (1894);  vol.  xxviii.  p.  437  (1896);  Elec- 
trical Engineer,  vol.  xviii.  p.  506  (1894). 


§73]  FORMS  OF  FIELD  MAGNETS.  281 

the  Zucker,  Levitt  &  Loeb  Company,1  New  York;  the  All- 
gemeine  Electric  Company2  (Dobrowolsky),  Berlin,  Germany; 
O.  L.  Kummer  &  Company,3  Dresden;  Garbe,  Lahmeyer  & 
Company,4  Aachen;  Elektricitats  Actien-Gesellschaft,  vor- 
mals  W.  Lahmeyer  &  Company,5  Frankfurt  a.  M. ;  Schuckert  & 
Company,6  Nuremburg;  C.  &  E.  Fein,7  Stuttgart;  Naglo 
Bros.,8  Berlin;  the  Zurich  Telephone  Company,9  Zurich;  the 
Oerlikon  Machine  Works,10  Zurich,  Switzerland;  R.  Alioth  & 
Company,11  Basel,  Switzerland;  the  Berlin  Electric  Construc- 
tion Company  (Schwartzkopff),12  Berlin,  Germany;  and  numer- 
ous others. 

In  Fig.  209  is  represented  the  Radial  Innerpole  Type,  which 
is  used  by  the  Siemens  &  Halske  Electric  Company,13  Chicago, 
111.,  and  Berlin,  Germany;  by  the  Alsacian  Electric  Construc- 
tion Company,14  Belfort,  Alsace;  by  Naglo  Bros.,15  Berlin, 
Germany;  by  Fein  &  Co.,16  Stuttgart,  Germany;  and  by  Ganz 
&  Co.,17  Budapest,  Austria. 

The  Tangential  Outerpole  Type,  Fig.  210,  is  employed  by  the 
Riker  Electric  Motor  Company,  Brooklyn;  by  the  Baxter 
Motor  Company,18  Baltimore,  Md. ;  the  Mather  Electric  Com- 
pany,19 Manchester,  Conn.;  the  Dahl  Electric  Motor  Com- 

1  "  Improved  American  Giant  Dynamo,"    Electrical  Age,  vol.  xviii.  p.  600 
{Oct.  17,  1896). 

2  Electrical  Engineer,  vol  xii.  p.  596  (1891);  vol.  xvi.  p.  103  (1893) 

3  Grawinkel  and  Strecker,  "  Hilfsbuch,"  fourth  edition,  p.  278. 
4Grawinkel  and  Strecker,  "  Hilfsbuch,"  fourth  edition,  p.  291. 
5  Grawinkel  and  Strecker,  "  Hilfsbuch,"  fourth  edition,  p.  294. 
*  Grawinkel  and  Strecker,  "  Hilfsbuch,"  fourth  edition,  p.  299. 

7  Grawinkel  and  Strecker,  "  Hilfsbuch,"  fourth  edition,  p.  304. 

8  Grawinkel  and  Strecker,  "  Hilfsbuch,"  fourth  edition,  p.  311. 

9  Grawinkel  and  Strecker,  "  Hilfsbuch,"  fourth  edition,  p.  327. 

10  Electrical  Engineer,  vol.  xii.  p.  597  (1891). 

11  Kittler,  "  Handbuch,"  vol.  i.  p.  934. 
12Kittler,  "  Handbuch,"  vol.  i.  p.  939. 

13  Electrical  World,  vol.  xxii.,  p.  61  (1893);  Electrical  Engineer,  vol.  xii.  p. 
572(1891);  vol.  xiv.  p.  313  (1892). 

14  L'Electricien,  vol.  i.  p.  33  (1891). 

15  Kittler,  "  Handbuch,"  vol.  i.  p.  916. 
™Zeitschr.  f.  Elektrotechn.,  vol.  v.  p.  545  (1887). 

17  Electrotechn.  Zeitschr.,  vol.  viii.  p.  233  (1887). 

18  Hering,  "  Electric  Railways,"  p.  294. 

19 Electrical  World,  vol.  xxiv.  p.  134  (1894);  Electrical  Engineer,  vol.  xviii. 
p.  177  (1894). 


282  DYNAMO-ELECTRIC  MACHINES.  [§73 

pany,1  New  York;  the  Electrochemical  and  Specialty  Com- 
pany,2 New  York  (/'Atlantic  Fan  Motor  "),  and  by  Cuenod, 
Sauter  &  Co.3  (Thury),  Geneva,  Switzerland;  generators  of 
this  type  are  further  used  in  the  power  station  of  the  General 
Electric  Company,4  Schenectady,  N.  Y.,  and  in  the  Herstal,5 
Belgium,  Arsenal. 

Machines  of  the  Tagential  Innerpole  Type,  Fig.  211,  are  built 
by  the  Helios  Electric  Company,6  Cologne,  Germany. 

In  the  Axial  Multipolar  Type,  Fig.  212,  there  are  usually  two 
magnets  for  each  pole,  one  on  each  side  of  the  armature,  in 
order  to  produce  a  symmetrical  magnetic  field.  This  form  is 
used  by  the  Short  Electric  Railway  Company,7  Cleveland,  O. ; 
Schuckert  &  Co.,8  Nuremberg,  Germany;  Fritsche  &  Pischon,9 
Berlin,  Germany;  Brush  Electric  Engineering  Company,1* 
London,  England  ("Victoria"  Dynamo);  by  M.  E.  Desro- 
ziers,11  Paris,  and  by  Fabius  Henrion,12  Nancy,  France.  The 
type  recently  brought  out  by  the  C.  &  C.  Electric  Company,13 
New  York,  has  but  one  magnet  per  pole,  and  the  polepieces 
are  arranged  opposite  the  external  circumference  of  the 
armature. 

Fig.  213  shows  the  Raditangent  Multipolar  Type,  which  is  a 
combination  of  the  Radial  and  Tangential  Outerpole  Types, 
Figs.  208  and  210  respectively,  and  which  is  employed  by  the 
Standard  Electric  Company,14  Chicago,  111. 


^Electrical  World,  vol.  xxi.  p.  213  (1893). 

2  Electrical  World,  vol.  xxi.  p.  394  (1893). 

3  Kittler,  "  Handbuch,"  vol.  i.  p.  936. 

4  Thompson,  "Dynamo-Electric  Machinery,"  fourth  edition,  p.  517. 

5  500  HP.  Generator,  Electrical  World,  vol.  xx.  p.  224  (1892). 

6  Kittler,  "  Handbuch,"  vol.  i.  p.  905. 

7  Electrical  World,  vol.  xviii.  p.  165  (1891). 

8  Elektrotechn.  Zeitsckr.,  vol.   xiv.  p.   513  (1893);  Electrical  Engineer,  vol. 
xii.  p.  595  (1891). 

9  Electrical  World,  vol.  xx.  p.  308  (1892);  Electrical  Engineer,  vol.  xii.  p. 
572  (1891). 

10  Thompson,  "  Dynamo  Electric  Machinery,"  fourth  edition,  p.  498. 

11  Electrical  Engineer,  vol.  xiv.  p.  259  (1892);  vol.  xv.  p.  340(1893). 
12Gravvinkel  and  Strecker,  "  Hilfsbuch,"  fourth  edition,  p.  317. 

13  Electrical  World,  vol.  xxviii.  p.  372  (1896). 

u  Electrical  World,  vol.  xxiii.  pp.  342,  549  (1894);  Electrical  Engineer,  vol. 
xvii.  pp.  189,  379  (1894). 


§  73]  FORMS  OF  FIELD  MAGNETS.  283 

If  only  one  magnet  is  used  in  multipolar  fields,  the  pole- 
pieces  may  be  so  shaped  as  to  face  the  armature  in  an  axial  or 
in  a  radial  direction.  In  the  former  case  the  Axial  Pole  Single 
Magnet  Multipolar  Typet  Fig.  214,  is  obtained,  which  is  used 
by  the  Brush  Electrical  Engineering  Company1  (Mordey), 
London,  England,  and  by  the  Fort  Wayne  Electric  Company  a 
(Wood),  Fort  Wayne,  Ind. 

In  the  latter  case  the  Outer- Inner  Pole  Single  Magnet 
Type,  Fig.  215,  results,  in  which  the  polepieces  may  either  all 
be  opposite  the  outer  or  the  inner  armature  surface,  or  alter- 
nately outside  and  inside  of  the  armature;  the  latter  arrange- 
ment, which  is  the  most  usual,  is  illustrated  in  Fig.  215,  and 
is  employed  by  the  Waddell-Entz  Company,3  Bridgeport, 
Conn.,  and  by  the  Esslinger  Works,4  Wurtemberg,  Germany; 
the  all  outerpole  arrangement  is  employed  in  the  direct  con- 
nected multipolar  type  of  the  C  &  C  Electric  Company,5  New 
York. 

If  two  magnets  furnish  the  magnetic  flux,  they  are  placed 
concentric  to  the  armature,  and  the  two  sets  of  polepieces  so 
arranged  that  adjacent  poles  on  either  side  of  the  armature 
are  of  unlike  polarity,  but  that  poles  facing  each  other  on 
opposite  sides  of  the  armature  have  the  same  polarity.  Such 
a  Double  Magnet  Multipolar  Type  is  shown  in  Fig.  216;  it  is 
that  designed  by  Lundell,6  and  built  by  the  Interior  Conduit 
and  Insulation  Company,  New  York. 

In  giving  the  yoke  of  the  Radial  Multipolar  Type  (Fig.  208) 
such  a  shape  as  to  form  a  polepiece  between  each  two  consec- 
utive magnets,  an  iron-clad  form  is  obtained  having  alternate 
salient  and  consequent  poles,  and  requiring  but  one-half  the 
number  of  magnets  as  a  radial  multipolar  machine  of  same 
number  of  poles. 

Fig.  217  shows  a  field  frame  of  the  Multipolar  Iron-clad 
Type,  having  six  poles,  which  is  the  form  employed  in  the 
gearless  street  car  motor  of  the  Short  Electric  Railway  Com- 

1  Thompson,  "  Dynamo  Electric  Machinery,"  fourth  edition,  p.  678. 

*  Electrical  Engineer   vol.  xv.  p.  46  (1893). 

3 Electrical  World,  vol.  xix.  p.  13  (1892);  vol.  xxii.  p.  120(1893). 

4Kittler,  "  Handbuch,"  vol.  i.  p.  945. 

5  Electrical  World,    vol.  xxv.  p.  33  (1895). 

' Electrical  World,  vol.  xx.  p.  85  (1892). 


284  D  YNA  MO-ELEC  TRIG  MA  CHINES.  [§  7  $ 

pany,1  Cleveland,  O.  In  Figs.  218  and  219,  two  special  cases 
of  this  type  .are  depicted,  both  representing  Fourpolar  Iron- 
clad Types,  and  differing  only  in  the  position  of  the  magnets. 
The  Horizontal  Fourpolar  Iron-clad  Type,  Fig.  218,  is  used  in 
the  Edison  Iron-clad  Motor  2  (General  Electric  Company),  and 
in  the  dynamos  of  the  Wenstrom  Electric  Company,3  Balti- 
more, Md.  The  Vertical  Fourpolar  Iron- clad  Type,  Fig.  219, 
is  employed  by  the  Elliott-Lincoln  Electric  Company,4  Cleve- 
land, O. 

Fig.  220  shows  a  special  case  of  the  Horizontal  Fourpolar 
Iron-clad  Type,  obtained  by  symmetrically  doubling  the  frame 
illustrated  in  Fig.  204,  and  providing  four  poles  instead  of 
two.  The  cores  are  so  wound  that  the  centre  of  the  cylindri- 
cal iron  wrappage  has  one  polarity  and  the  ends  the  opposite 
polarity.  Two  oppositely  situated  polepieces  are  joined  to  the 
middle,  and  the  two  sets  of  intermediate  ones  to  the  ends  of 
the  magnet  frame;  the  lower  half  of  Fig.  220,  consequently, 
is  a  section  taken  at  right  angles  to  the  upper  half,  the  diamet- 
rically opposite  section  being  identical.  This  type  has  been 
developed  by  the  Storey  Motor  and  Tool  Company,5  New 
York. 

Multipolar  fields  may  also  be  formed  by  a  number  of  inde- 
pendent horseshoes  arranged  symmetrically  around  the  outer 
armature  periphery.  Figs.  221  and  222  show  two  such  Mul- 
tiple Horseshoe  Types,  double  magnet  horseshoes  being  employed 
in  the  former,  and  single  magnet  horseshoes  in  the  latter  type. 
Multiple  horseshoe  machines  of  the  double  magnet  form  (Fig. 
221)  have  been  designed  by  Elphinstone  &  Vincent,  and  by 
Elwell-Parker  Electric  Construction  Corporation,6  England; 
while  the  single-magnet  form  (Fig.  222)  is  employed  by  the 
Electron  Manufacturing  Company7  (Ferret),  Springfield,  Mass. 


1  Electrical  World,  vol.  xx.  p.  241  (1892);    Electrical  Engineer,  vol.  xiv.  p. 
395  (1895). 

*  Electrical  Engineer,  vol.  xii.  p.  598  (1891). 
^Electrical  World,  vol.  xxiv,  p.  183  (1894). 

4 Electrical  World,  vol.  xxi.  p.  193  (1893);  vol.  xxii.  p.  484  (1893). 
5  Electrical  World,   vol.   xxi.  p.  214(1893);  Electrical  Engineer,   vol.  xv.  p. 
263  (1893). 

*  7^he  Electrician  (London),  vol.  xxi.  p.  183  (1888), 

7 Electrical  Engineer,  vol.  x.  p.  592  (1890);  vol.  xiii.  p.  2  (1892). 


§  74]  FORMS  OF  FIELD  MAGNETS.  285 

Further  forms  of  multipolar  fields  can  be  derived  from  the 
bipolar  horizontal  and  vertical  double  magnet  types  respec- 
tively. If,  in  the  Vertical  Double  Magnet  Type,  Fig.  196,  an 
additional  polepiece  is  provided  at  the  centre  of  the  frame  so 
as  to  face  the  internal  surface  of  the  armature  at  right  angles 
to  the  outer  polepieces,  the  Fourpolar  Vertical  Double  Magnet 
Type  is  created,  which,  when  laid  on  its  side,  will  constitute 
the  Fourpolar  Horizontal  Double  Magnet  Type,  Fig.  223.  If,  in 
the  Vertical  Double  Magnet  Type,  Fig.  199,  the  two  cores  are 
cut  in  halves  and  additional  polepieces  inserted  at  right  angles 
to  the  existing  ones,  the  Vertical  Quadruple  Magnet  Type,  Fig. 
224,  is  obtained;  the  same  operation  performed  with  the  Hori- 
zontal Double  Magnet  Type,  Fig.  197,  will  give  the  Horizontal 
Quadruple  Magnet  Type. 

Fourpolar  Horizontal  Double  Magnet  Dynamos,  Fig.  223,  are 
built  by  the  Zurich  Telephone  Company,1  Zurich,  Switzerland; 
and  Vertical  Quadruple  Magnet  Machine,  Fig.  224,  by  the 
Duplex  Electric  Company,2  Corry,  Pa. 

Numerous  other  multipolar  types  have  been  invented  and 
patented,  but  either  are  of  historical  value  only,  or  have  not 
yet  come  into  practical  use. 

74.  Selection  of  Type. 

If  the  type  is  not  specified,  the  field  magnet  frame  for  a 
large  output  machine  should  be  chosen  of  one  of  the  multipolar 
types,  as  in  these  the  advantage  of  a  better  proportioning  and 
a  higher  efficiency  of  the  armature  winding,  and  the  possibility 
of  a  symmetrical  arrangement  of  the  magnetic  frame,  results 
in  a  saving  of  copper  as  well  as  of  iron;  while  for  smaller 
machines  — below  10  KW  capacity — the  bipolar  forms  are  pref- 
erable on  account  of  the  great  complication  caused  by  the 
increased  number  of  armature  sections,  commutator-divisions, 
field  coils,  etc.,  necessary  in  multipolar  machines,  and  on 
account  of  the  narrowness  of  the  neutral  or  non-sparking 
space  on  a  multipolar  commutator. 

The  field,  moreover,  should   have  as  few  separate  magnetic 


!Kittler,  "  Handbuch,"  vol.  i.  p.  947. 

^Electrical  World,  vol.  xx.  p.  14(1892);  Electrical  Engineer,  vol.  xiv.  p, 
I  (1892). 


286  DYNAMO-ELECTRIC  MACHINES.  [§74 

circuits  as  possible;  thus,  in  the  case  of  a  bipolar  type,  it 
should  be  a  single  magnetic  circuit  rather  than  the  consequent 
pole  type  which  is  formed  by  two  or  more  magnetic  circuits,  of 
one  or  two  magnets  each,  in  parallel,  because  the  former  is 
more  economical  in  wire  and  in  current  required  for  excita- 
tion. In  two-circuit  consequent  pole  machines,  for  instance, 
such  as  the  double  magnet  types,  Figs.  197,  199,  and  200,  and 
the  double  horseshoe  types,  Figs.  201  and  202,  according  to 
Table  LXIX.,  §  75,  there  is  1.41  times  the  length  of  wire,  and 
consequently  also  1.41  times  the  energy  of  magnetization 
required  than  in  a  single  circuit,  round  cores  being  used  in 
both  cases,  and  the  single  circuit  having  exactly  twice  the  area 
of  each  of  the  two  parallel  circuits  in  the  consequent  pole  ma- 
chines. Triple  and  quadruple  magnetic  circuits,  /.  e.,  3  or  4 
cores,  or  sets  of  cores,  magnetically  in  parallel,  are  still  more 
objectionable,  requiring,  when  the  cores  are  of  circular  cross- 
section,  1.73  and  2.00  times  as  much  wire,  respectively,  as  a 
single  magnetic  circuit  having  a  round  core  of  equal  total  sec- 
tional area. 

If  a  machine  has  several  magnetic  circuits,  each  of  which, 
however,  passes  through  all  the  magnets  in  series,  then  the 
frame  is  to  be  considered  as  consisting  of  but  one  single  cir- 
cuit, for  the  subdivision  only  takes  place  in  the  yokes,  and  it 
is  immaterial  as  to  the  length  of  exciting  wire  whether  the 
return  path  of  a  single  circuit  is  formed  by  one  yoke,  or  by  a 
number  of  yokes  magnetically  in  parallel.  The  above-named 
objection  to  divided  circuit  types,  consequently,  does  not 
apply  in  the  case  of  the  iron-clad  forms,  Figs.  203  to  207. 

According  to  Table  LXVIII.,  §  70,  the  horizontal  double 
magnet  type,  Fig.  195,  and  the  horizontal  iron-clad  type, 
Fig.  203,  are  the  best  bipolar  forms,  magnetically.  The  iron- 
clad types,  furthermore,  possess  the  mechanical  advantage  of 
having  the  field  windings  and  the  armature  protected  from 
external  injuries  by  the  frame  of  the  machines,  which  makes 
them  eminently  adaptable  to  motors  for  railway,  mining,  and 
similar  work. 

The  inverted  horseshoe  type,  Fig.  188,  which  ranks  very 
highly,  as  far  as  its  magnetic  qualities  are  concerned,  has  the 
centre  of  its  armature  at  a  comparatively  very  great  distance 
from  the  base,  requiring  very  high  pillow-blocks,  which  have 


§74]  FORMS  OF  FIELD  MAGNETS.  287 

to  carry  the  weight  as  well  as  the  downward  thrust  of  the 
armature  inherent  to  the  inverted  forms  having  the  field  wind- 
ings below  the  centre  of  revolution;  see  §  42.  The  side  pull 
of  the  belt  with  a  high  centre  line  of  shaft  tends  to  tip  the 
machine,  and  the  changes  in  the  pull  due  even  to  the  undula- 
tions of  the  belt  will  cause  a  tremor  in  the  frame  which  jars 
the  brushes,  and,  eventually,  loosens  their  holders,  and  which 
has  a  disastrous  influence  upon  the  wearing  of  the  commutator. 
On  this  account  the  inverted  forms,  or  Bunder-types,"  can 
only  be  used  for  small  and  medium-sized  machines,  in  which 
the  height  of  the  pillow-blocks  remains  within  practical 
limits. 

In  selecting  a  multipolar  type,  Table  LXVIII.  shows  that  the 
radial  innerpole  type,  Fig.  209,  offers  the  best  advantage 
with  regard  to  the  magnetical  disposition;  with  this  type, 
however,  are  connected  some  mechanical  difficulties,  due  to 
the  necessity  of  supporting  the  frame  from  one  of  its  ends, 
laterally,  and  the  armature  from  the  other. 

In  the  outerpole  types  the  armature  core  can  be  supported 
centrally  from  the  inner  circumference,  and  the  frame  suit- 
ably provided  with  external  lugs  or  flanges  resting  upon  the 
foundation,  a  most  desirable  arrangement  for  mechanical 
strength  and  convenience.  The  most  favorite  of  the  out- 
erpole forms  is  the  radial  outerpole  type,  Fig.  208,  on 
account  of  its  superiority,  magnetically,  over  the  tangential 
and  axial  multipolar  types. 

In  all  dynamo  designs  the  consideration  is  especially  to  be 
borne  in  mind  that  the  whole  machine  as  well  as  its  various 
parts  should  be  easily  accessible  for  inspection,  and  so  arranged 
that  they  can  conveniently  be  removed  for  repair  or  exchange. 
A  large  number  of  machines  owe  their  popularity  chiefly  to 
their  good  disposition  in  this  respect. 

The  shape  of  the  frame  in  all  cases  is  preferably  to  be  so 
chosen  that  the  length  of  the  magnetic  circuit  in  the  same  is  as 
short  as  possible. 


CHAPTER  XV. 

GENERAL    CONSTRUCTION    RULES. 

75.  Magnet  Cores. 

a.   Material. 

The  field  cores  should  preferably  be  of  wrought  iron,  or  of 
cast  steel,  in  order  to  economize  in  magnet  wire,  for  the  use  of 
cast  iron,  on  account  of  its  low  permeability,  would  require 
cores  of  at  least  if,  *'.  <?.,  almost  twice  the  cross-section,  and 
therefore  a  much  greater  length  of  wire,  to  obtain  the  neces- 
sary magnetizing  force.  With  the  smaller  wrought-iron  cores 
the  leakage  would  also  be  less. 

In  spite  of  the  decided  advantage  of  wrought-iron  cores, 
cast-iron  field  magnets  are  very  common,  since  the  temptation 
to  use  castings  instead  of  forgings  is  very  great.  Where 
weight  and  bulk  are  of  no  consequence,  a  cast-iron  field  mag- 
net may  prove  nearly  as  economical  as  one  of  wrought  iron 
costing  considerably  more,  but  the  former  requires  from  \ 
to  %  times  more  wire  to  encircle  it  than  a  wrought-iron  one 
of  similar  magnetic  density,  in  case  of  circular  cross-section, 
and  it  is  evident  that  this,  by  introducing  additional  electrical 
resistance,  will  prove  a  constant  source  of  unnecessary  running 
expense. 

As  to  the  use  of  steel  in  dynamos,  H.  F.  Parshall,  in  a  paper 
delivered  before  the  Franklin  Institute,1  states  that  magnet 
frames  made  of  cast  steel  are  25  per  cent,  cheaper  than  those 
of  cast  iron,  but  possess  the  disadvantage  of  being  not  as  uni- 
form in  magnetic  qualities  as  cast  iron.  He  further  asserts 
that  good  cast  steel  should  not  have  greater  percentages  of 
impurities  than  .25  per  cent,  of  carbon,  .6  per  cent,  of  man- 
ganese, .2  per  cent,  of  silicon,  .08  per  cent,  of  phosphorus, 
and  .05  per  cent,  of  sulphur.  The  effect  of  carbon  is  to  lessen 
the  magnetic  continuity  and  to  greatly  reduce  the  permeability; 


1  Electrical  World,  vol.  xxiii.  p.  214,  February  17,  1894. 


§75]  GENERAL   CONSTRUCTION  RULES.  289 

carbon,  therefore,  is  the  most  objectionable  impurity,  and,  if 
possible,  should  be  restricted  to  smaller  amounts  thaTi  the 
maximum  above  quoted.  Manganese,  in  quantities  larger  than 
stated,  seriously  reduces  the  magnetic  susceptibility  of  the 
steel,  a  12  per  cent,  mixture  having  scarcely  greater  suscepti- 
bility than  air.  Silicon  is  objectionable  through  facilitating 
the  formation  of  blowholes,  and  from  its  hardening  effect. 

E.  Schulz,1  in  comparing  two  dynamos  differing  only  in  the 
material  of  the  field  frame  and  in  the  magnet  winding,  finds 
that  the  weight  of  a  cast-steel  magnet  frame  is  about  one-half 
of  that  of  cast  iron,  and  that  the  weight  of  the  copper  for  the 
magnets,  on  account  of  the  smaller  cross-section  and  the 
greater  permeability  of  the  cast  steel,  is  reduced  to  somewhat 
less  than  one-half.  The  price  of  the  frame  will  accordingly  be 
about  ij-  times  that  of  the  cast-iron  one,  but,  on  account  of 
the  reduction  of  the  copper  weight,  the  cost  of  the  whole  ma- 
chine will  be  less  for  a  cast-steel  than  for  a  cast-iron  frame,  the 
total  weight  being  less  than  one-half  in  the  former  case. 

According  to  Professor  Ewing2  the  permeability  of  good 
cast  steel  at  low  magnetic  forces  is  less  than  that  of  wrought 
iron,  but  the  reverse  is  the  case  with  high  forces.  In  a 
specially  good  sample  tested  by  G.  Kapp  and  Professor 
Ewing,  a  magnetic  density  of  18,000  lines  per  square  centimetre 
(=  116,000  lines  per  square  inch)  was  reached,  with  but  little 
more  than  one-half  the  magnetizing  force  as  is  necessary  for 
the  same  induction  in  ordinary  wrought  iron. 

b.  Form  of  Cross- Section. 

The  best  form  of  cross-section  for  a  magnet-core  is  undoubt- 
edly that  which  possesses  the  smallest  circumference  for  a 
given  area,  and  this  most  economical  section  is  the  circle.  It 
is,  however,  often  preferable  on  account  of  reducing  the  dimen- 
sion of  the  machine  perpendicular  to  the  armature  shaft,  to 
use  cores  of  other  than  circular  section;  in  this  case  either 
rectangular,  elliptical,  or  oval  cores  are  employed,  or  several 


1  Elektrisches  Echo,  August  n,  1894;  Electrical  World,  vol.  xxiv.,  p.  238 
(September  8,  1894). 

'2  Electrical  Engineer,  London,  October  5,  1894;  Electrical  World,  vol. 
xxiv.  p.  446  (October  27,  1894). 


290  DYNAMO-ELECTRIC  MACHINES.  [§75 

round  cores  are  placed  side  by  side  and  connected  in  parallel 
to  each  other,  magnetically.  The  latter  method,  however,  is 
not  recommendable  for  the  reason  that  the  magnetizing  effects 
of  the  neighboring  coils  partly  neutralize  each  other,  because 
of  the  currents  of  equal  polarity  flowing  in  opposite  lateral 
directions  in  the  parts  of  the  coils  facing  each  other,  as  indi- 
cated by  arrows  in  Fig.  225.  There  is,  consequently,  a  double 

ooo 

Fig.  225. — Direction  of  Current  in  Parallel  Magnet  Cores  of  same  Polarity. 

loss  connected  with  this  arrangement,  a  larger  expenditure 
of  copper,  connected  with  higher  magnet  resistance,  and 
decrease  of  the  magnetizing  effects  by  mutual  influence  of  the 
coils. 

Besides  the  forms  mentioned,  also  square  cores  and  hollow 
magnets  of  ring-section  are  frequently  used. 

An  idea  of  the  economy  of  the  form  of  cross-section  to  be 
chosen  can  be  formed  by  means  of  the  following  Table  LXIX., 
which  gives  the  circumferences  for  unit  area  of  the  various 
forms  of  cross-sections  employed  in  modern  machines,  and 
compares  the  same  with  the  circumference  of  the  most  eco- 
nomical form,  the  circle.  In  the  case  of  rectangular  and  elliptical 
cores,  four  forms  each  are  considered,  the  lengths  being,  re- 
spectively, 2,  3,  4,  and  8  times  the  width  of  the  sections.  For 
vval  cores  three  sections  are  examined,  the  semicircular  end 
portions  being  attached  to  a  centre  portion  formed  of  i,  2,  and 
4  adjacent  squares,  respectively.  Next  come  four  sections 
consisting  of  several  round  cores  in  parallel,  namely,  2,  3,  4,  and 
8  separate  circles.  Of  hollow  cores,  finally,  five  cases  are  con- 
sidered, the  internal  diameter  being,  respectively,  i,  2,  3,  4, 
and  8  times  the  radial  thickness  of  the  cross-section. 

Hollow  Magnets  are  used  in  some  special  types,  such  as 
shown  in  Figs.  84,  94,  95,  96,  and  100,  where  large  circumfer- 
ences of  the  cores  are  required  but  not  the  total  area  inclosed 
by  these  circumferences,  and  where  the  armature  or  its  shaft 
has  to  pass  through  the  centre  of  the  magnet. 

As  to  the  use  of  hollow  magnets  in  place  of  solid  ones,  Profes- 


§76] 


GENERAL   CONSTRUCTION  RULES. 


291 


TABLE  LXIX. — CIRCUMFERENCE  OF  VARIOUS  FORMS  OF  CROSS. SECTIONS 

OF  EQUAL  AREA. 


Form  of 
Cross-Section 

Description 

Circumference 
for 
Unit  Area 

Relative 
Circumference 
(Circle  =1) 

% 

Circle 

3.545 

1 

Hi 

Square 

4.000 

1.13 

Rectangle,  1:2 

4.243 

1.20 

1:3 

4.62 

1.305 

1:4 

5.00 

1.41 

vmmm%% 

1:8 

6.364 

1.80 

Ellipse,        1:2 

3.87 

1.09 

1:3 

4.35 

1.23 

1:4 

4.84 

1.37 

«^mj^ 

1:8 

6.53 

1.84 

OvaUsqu.2^; 

3.85 

1.085 

%M%% 

„    2    •<    2     " 

4.28 

1.21 

mmm> 

,,    4   "    2      - 

5.09 

1.44 

H  H 

2  Circles 

5.01 

1.41 

©  0  © 

3       " 

6.14 

1.73 

©  ©  ©  © 

4       " 

7.09 

2.00 

©  ©  @  © 
©  ©  ©  © 

8       " 

10.03 

2.83 

B 

Ring,           1:1 

3.85 

1.085 

Q 

1:2 

4.09 

1,155 

0 

1:3 

4.43 

1.25 

0 

1:4 

4.76 

1.34 

0 

1:8 

5.91 

1.67 

sor  Grotrian1  states  that  with  weak  magnetizing  forces  only  the 
outer  layers  of  the  iron,  next  to  the  winding,  are  magnetized. 

1  Elektrotechn.  Zeitschr.,  vol.  xv.  p.  36  (January  18,  1894);  Electrical  World, 
vol.  xxiii.  p.  216  (February  17,  1894). 


292  DYNAMO-ELECTRIC  MACHINES.  [§75 

E.  Schulz,1  however,  showed  by  practical  experiments  that  the 
magnetization  is  exactly  proportional  to  the  area  of  the  core- 
section,  even  at  the  low  induction  due  to  the  remanent  mag- 
netism; from  this  can  be  concluded  that  Professor  Grotrian's 
results  do  not  apply  to  the  case  of  dynamo  magnets  under  prac- 
tical conditions.  A.  Foppl 2  claims  that  the  theory  of  Professor 
Grotrian  is  correct,  /.  e.,  that  the  fl-ux  gradually  penetrates 
the  magnet  from  its  circumference,  and  that  under  certain  cir- 
cumstances it  may  not  reach  the  centre  of  the  core,  but  he 
admits  that  this  theory  has  no  practical  bearing  upon  such 
magnets  as  are  now  used  in  practical  dynamo  design. 

c.  Ratio  of  Core-area  to  Cross-section  of  Armature. 

The  relation  between  the  cross-section  of  iron  in  the  magnet 
cores  to  that  of  the  armature  core  is  a  very  important  one,  as 
on  its  proper  adjustment  depends  the  attainment  of  maximum 
output  per  pound  of  wire  with  minimum  weight  of  iron. 

According  to  tests  made  at  the  Cornell  University  under  the 
direction  of  Professor  Dugald  C.  Jackson,3  the  best  area  of 
cross-section  of  the  magnet  cores  for  drum  machines  is  ii 
times  that  of  least  cross-section  of  armature,  if  the  cores  are 
of  good  wrought  iron,  or  about.  2j  times  the  minimum  arma- 
ture section  if  cast  iron  cores  are  used. 

According  to  Table  XXII.,  §  26,  the  maximum  core  den- 
sity in  ring  armatures  is  from  i^  to  if  times  that  of  drum 
armatures;  for  equal  amounts  of  active  wire,  therefore,  the 
former  require  i^  to  if  times  as  great  a  magnetic  flux 
as  the  latter,  and  the  cross-sections  of  the  magnet  cross,  con- 
sequently, have  to  be  taken  correspondingly  greater  in  case  of 
ring  machines,  namely,  i|-  to  2}  times  the  minimum  armature 
section  in  case  of  wrought  iron  cores,  and  3  to  4  times  the  arma- 
ture section  for  cast  iron  field  magnets. 

Professor  S.  P.   Thompson,   in  his    "Manual  on   Dynamo- 


1  Elektrotechn.  Zeitschr.,  vol.  xv.  p.  50  (February  8,  1894);  Electrical  World, 
vol.  xxiii.  p.  337  (March  10,  1894). 

2  Elektrotechn.  Zeitschr.,  vol.  xv.  p.  206  (April  12,  1894);  Electrical  World, 
vol.  xxiii.  p.  680  (May  19,  1894). 

3  Transactions  Am.  Inst    of  El.  Eng.,  vol.  iv.  (May  18,  1887);  Electrical 
Engineer,  vol.  iii.  p.  221  (June,  1887). 


§  76]  GENERAL   CONSTRUCTION  RULES.  293 

Electric  Machinery,"  l  gives  1.25  for  wrought  iron  and  2.3  for 
cast  iron  as  the  usual  ratio  in  drum  machines,  and  1.66  and  3 
respectively,  in  ring-armature  dynamos. 

In  the  experiments  conducted  by  Professor  Jackson,  ten 
different  armatures,  all  of  same  length  and  same  external 
diameter,  but  of  different  bores,  were  used  in  the  same  field, 
thus  including  a  range  of  from  .5  to  1.4  for  the  ratio  of  least 
armature  section  to  core  area.  The  curves  obtained  show  that 
the  total  induction  through  the  armature  increased  quite  rapidly 
when  the  armature  was  increased  in  area  from  .5  of  that  of  the 
magnets  to  about  .  75  of  the  core  area.  From  .75  to  . 9  there  is 
still  an  increase  of  induction  with  increase  of  armature  section, 
though  comparatively  small,  and  beyond  .9  the  increase  is  of 
no  practical  importance. 

76.    Polepieces. 

a.   Material. 

The  polepieces,  if  the  shape  and  the  construction  of  the 
magnet  frame  permits,  should  be  of  wrought  iron  or  cast  steel,  in 
order  to  reduce  their  size,  and  therefore  their  magnetic  leak- 
age, they  being  of  the  highest  magnetic  potential  of  any  part 
of  the  magnetic  circuit.  In  forging,  care  should  be  taken  that 
the  "grain"  or  texture  of  the  iron  runs  in  the  direction  of  the 
lines  of  force.  The  polepieces,  however,  usually  have  to  em- 
brace from  .7  to  .8  of  the  armature  surface  (compare  §15), 
and  are,  therefore,  particularly  in  the  case  of  bipolar  machines, 
often  comparatively  large.  If  in  such  a  case  their  cross-sec- 
tion, in  order  to  give  sufficient  mechanical  strength,  is  to  be 
far  in  excess  of  the  area  needed  for  the  magnetic  flux,  there 
is  no  gain  in  using  wrought  iron  or  cast  steel,  and  the  pole- 
pieces  should  be  made  of  cast  iron.  The  cast  iron  used  shouTd 
be  as  soft  and  free  from  impurities  as  possible.  It  is  prefer- 
able, whenever  practicable,  to  have  it  annealed,  and,  if  not  toa 
large  in  bulk,  to  have  it  converted  into  malleable  iron;  this  is 
especially  to  be  recommended  for  small  machines. 

An  admixture  of  aluminum  has  been  found  to  increase  the 
permeability  of  the  cast  iron;  by  adding  i£  per  cent.,  by 
weight,  of  aluminum,  the  maximum  carrying  capacity  of  the 


!S.  P.  Thompson,  "  Dynamo-Electric  Machinery,"  fifth  edition,  p.  378. 


294  DYNAMO-ELECTRIC  MACHINES.  [§76 

cast  iron  is  increased  about  5  per  cent. ;  by  3  per  cent,  admix- 
ture it  is  increased  7  per  cent. ;  and  by  adding  6  per  cent,  of 
aluminum,  the  induction  increases  about  9  per  cent. ;  above  7 
per  cent,  of  admixture  the  permeability  decreases,  and  at  12 
per  cent,  addition  of  aluminum  the  gain  in  magnetic  conduc- 
tivity falls  down  to  7  per  cent.  From  this  it  follows  that  an 
addition  of  from  6  to  7  per  cent.,  by  weight,  of  aluminum  is 
the  proper  admixture  for  the  purpose  of  improving  the  mag- 
netic qualities  of  cast  iron,  which  is  explained  by  the  fact  that 
the  latter  percentage  is  the  limit  from  which  up  the  hardening 
influence  of  the  aluminum  upon  the  cast  iron  becomes  appre- 
ciable. 

In  large  multipolar  machines  combination  frames  consisting 
of  wrought-iron  magnet  cores,  cast-iron  yokes,  and  cast-steel 
polepieces  give  excellent  results,  having  the  advantages  of 
the  high  permeability  and  uniformity  in  the  magnetic  qualities 
of  the  wrought  iron,  of  cheapness  of  the  cast  iron,  and  of  re- 
duction in  size  of  the  cast-steel  polepieces,  and  being  easier 
to  machine,  requiring  less  chipping,  and  being  more  easily  fin- 
ished than  a  magnet  frame  made  entirely  of  cast  steel. 

A  material  which  a  few  years  ago  was  quite  a  favorite  with 
dynamo  builders,  but  which  since  has  to  a  great  extent  been 
displaced  by  the  cheaper  cast  steel,  is  the  so-called  "  Mitis 
metal,"  or  cast  wrought  iron,  obtained  by  melting  down  scrap 
wrought  iron  in  crucibles,  and  by  rendering  it  fluid  by  the 
addition  of  a  small  quantity  of  aluminum.  The  trouble  with 
this  material  was  that  a  great  many  extra  precautions  had  to 
be  taken  to  procure  sound  castings,  and  that  as  a  rule  the 
castings  were  rough  and  difficult  to  work  on  account  of  their 
toughness.  The  magnetic  value  of  Mitis  iron  differs  very 
little  from  that  of  cast  steel,  its  permeability  at  the  inductions 
used  in  practice  being  but  a  trifle  lower  than  that  of  the  latter. 

Edges  and  sharp  corners  are  to  be  avoided  as  much  as  pos- 
sible, for  if  they  protrude  sufficiently  they  will  act  to  a  certain 
extent  as  poles,  and  give  cause  to  a  source  of  loss.  In  cast- 
ings thin  projections  are  apt  to  chill  while  being  cast,  thus 
making  them  quite  hard  and  destroying  their  magnetic  quali- 
ties; when  necessary  for  mechanical  reasons,  they  should, 
therefore,  be  cast  quite  thick  and  massive,  and  may  afterward 
be  planed  or  turned  down  to  the  required  size. 


§  76]  GENERAL    CONSTRUCTION  RULES.  295 

b.   Shape. 

The  polepieces  have  for  their  object  the  transmission  to 
the  armature  of  the  magnetic  flux  set  up  by  the  field  magnet, 
and  the  establishment  of  a  magnetic  field  space  around  the 
armature.  The  shape  to  be  given  to  them  must,  therefore, 
effect  the  concentration  of  the  lines  of  force  upon  the  arma- 
ture, and  not  their  diffusion  through  the  air.  This,  in  general, 
is  achieved  by  making  the  polar  surfaces  as  large  as  possible, 
and  bringing  them  as  near  to  the  armature  as  mechanical  con- 
siderations permit,  and  by  reducing  the  leakage  areas  of  the 
free  pole  surfaces  as  much  as  possible.  For  practical  rules  of 
fixing  the  distance  between  the  pole  corners  and  the  clearance 
between  armature  surface  and  polepieces  for  various  kinds 
and  sizes  of  armatures,  see  Tables  LX.  and  LXL,  §  58,  re- 
spectively. 

Since  eddy  currents  are  produced  in  all  metallic  masses, 
either  by  their  motion  through  magnetic  fields  or  by  variations 
in  the  strength  of  electric  currents  flowing  near  them,  the  pole- 
pieces  of  a  dynamo-electric  machine  are  seats  of  such  currents, 
which  form  closed  circuits  of  comparatively  low  resistance, 
and  thereby  cause  undue  heating.  These  currents  are  strong- 
est where  the  changes  in  the  intensity  of  the  magnetic  field  or 
of  the  electric  current  are  the  greatest  and  the  most  sudden; 
this  is  the  case,  and  consequently  the  eddy  currents  are  strong- 
est at  those  corners  of  the  polepieces  from  which  the  arma- 
ture is  moved  in  its  rotation,  for,  owing  to  the  distortion  of 
the  magnetic  field  by  the  revolving  armature,  a  density  greater 
than  the  average  is  created  at  the  corners  where  the  armature 
leaves  the  polepieces,  and  a  density  smaller  than  the  average 
at  the  corners  where  it  enters.  In  order  to  reduce  and 
eventually  to  avoid  the  generation  of  these  eddy  currents  in 
the  polepieces,  as  well  as  in  the  armature  conductors,  it  is 
therefore  necessary  to  prevent  the  crowding  of  the  mag- 
netic lines  toward  the  tips  of  the  polepieces,  and  to  so  arrange 
the  poles  that  the  magnetic  field  does  not  suddenly  fall 
off  at  the  pole  corners,  but  gradually  decreases  in  strength 
toward  the  neutral  zone.  This  object  in  a  smooth  arma- 
ture machine  can  be  attained  (i)  by  gradually  increasing 
the  air  gap  from  the  centres  of  the  poles  toward  the 


296 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§76 


neutral  spaces  in  boring  the  polar  faces  to  a  diameter  larger 
than  their  least  diametrical  distance  apart,  thus  giving  an 
elliptical  shape  to  the  field  space,  as  illustrated  in  Fig.  226;  (2) 
by  providing  wrought  iron  polepieces  with  cast  iron  tips  form- 
ing the  pole  corners  and  terminating  the  arcs  embraced  by  the 
pole  faces  (see  Figs.  227  and  228);  or  (3)  by  establishing  a 
magnetic  shunt  between  two  neighboring  poles  in  connecting 
the  polepieces,  either  by  a  cast-iron  ring  of  small  sectional 


FIG  226      FiQ.227 


FIQ.  228 


FlQ  229 


FlQ.  235 


FIG.  236 


FIG.  237 


Figs.  226  to  237. — Types  of  Polepieces. 

area  (Dobrowolsky's  pole-bushing]  or  by  placing  thin  bridges 
across  the  neighboring  pole  corners,  as  shown  in  Figs.  229  and 
230,  respectively. 

The  ellipsity  of  the  field  space  has  the  advantage  that  it  con- 
fines the  lines  of  force  within  the  sphere  of  the  pole  faces  by 
proportionately  increasing  the  reluctance  toward  the  pole  cor- 
ners, thus  preventing  an  increase  of  the  magnetic  density  at 
any  particular  portion  of  the  polepiece.  The  application  of 
cast-iron  pole  tips  with  wrought  iron  (or  cast-steel)  polepieces 
does  not  prevent  the  crowding  of  the  lines  at  the  pole  corners, 
but,  by  reason  of  the  low  permeability  of  the  cast  iron,  re- 
duces their  density  to  a  figure  below  that  in  the  wrought  iron, 
and  consequently  effects  a  graduation  of  the  field  strength 
near  the  neutral  space,  the  maximum  density  being  in  the 


§  76]  GENERAL   CONSTRUCTION  RULES.  297 

wrought  iron  at  the  point  where  the  cast-iron  tips  are  joined. 
In  the  pole  bushing  or  its  equivalent,  the  pole  bridges,  the  re^ch 
of  the  magnetic  field  is  greatly  increased,  the  percentage  of 
the  polar  arc  being  practically  —  100,  and  also  a  more  or  less 
gradual  decrease  of  the  field  strength  at  the  neutral  point  is 
obtained,  but  the  length  of  the  non-sparking  space  is  greatly 
reduced  and  thereby  its  uncertainty  increased,  thus  making 
the  proper  setting  of  the  brushes  a  very  difficult  operation. 

It  has  also  been  recommended  to  laminate  both  the  polepieces 
and  the  magnet  cores  in  the  direction  parallel  to  the  armature 
shaft,  in  order  to  prevent  the  production  of  eddy  currents,  but 
this  can  only  be  applied  to  small  dynamos,  as  the  additional 
cost  connected  with  such  a  lamination  in  large  machines  would 
be  in  no  proportion  to  the  small  gain  obtained.  Besides, 
there  is  another  reason  against  lamination :  a  laminated  magnet 
frame  is  very  sensitive  to  the  fluctuations  in  the  load  of  the 
machine,  which  naturally  react  upon  the  magnetic  field,  and  in 
following  these  fluctuations  an  unsteady  magnetization  is  pro- 
duced, which,  in  turn,  again  tends  to  increase  the  fluctuations 
causing  its  variability;  while  in  a  solid  magnet  frame  the  eddy 
currents  induced  by  the  changes  of  magnetization  caused  by 
the  fluctuations  of  the  load  tend  to  counteract  the  very  changes 
producing  them,  and  therefore  exercise  a  steadying  influence 
upon  the  field,  thus  reducing  the  fluctuations  in  the  external 
circuit  of  the  machine. 

An  expedient  sometimes  used  instead  of  laminating  the  pole- 
pieces  is  to  cut  narrow  longitudinal  slots  in  the  polepieces, 
Fig.  231,  thus  laminating  a  portion  of  the  polepieces  only. 
These  slots  at  the  same  time  serve  to  increase  the  length  of 
the  path  traversed  by  the  lines  of  force  set  up  by  the  action  of 
the  armature  current,  and  to  thus  reduce  the  armature  reaction 
upon  the  magnetic  field,  checking  the  sparking  connected 
therewith. 

When  the  commutator  brushes,  after  having  short-circuited 
an  armature  coil,  break  this  short  circuit,  the  sudden  reversal 
of  the  current  in  the  same,  produced  in  passing  the  neutral 
line  of  the  field,  together  with  the  self-induction  set  up  by  the 
extra  current  on  breaking,  causes  a  spark  to  appear  at  the 
brushes,  which  maybe  considerable,  since  in  the  comparatively 
low  resistance  of  the  short-circuited  coil  a  small  electromotive 


298  DYNAMO-ELECTRIC  MACHINES.  [§76 

force  is  sufficient  to  produce  a  heavy  current.  If  a  dynamo, 
therefore,  is  otherwise  well  designed,  that  is,  if  the  armature 
is  subdivided  into  a  sufficient  number  of  sections,  if  the  field 
is  strong  enough  so  as  not  to  be  overpowered  by  the  armature, 
and  if  the  thickness  of  the  brushes  is  so  chosen  as  to  not  short- 
circuit  more  than  one  or  two  armature  sections  each  simulta- 
neously, and  as  not  to  leave  one  commutator-bar  before  making 
connection  with  the  next  strip,  then  the  sparking  at  the  com- 
mutator can  be  reduced  to  a  practically  unappreciable  degree 
by  so.  shaping  the  pole  surfaces  as  to  give  a  suitable  fringe  of 
magnetic  field  of  graduated  intensity,  thus  not  only  causing 
the  current  in  the  short-circuited  coils  to  die  out  by  degrees, 
but  also  compelling  the  coils  to  enter  the  field  of  opposite 
polarity  gradually.  This  is  achieved  by  giving  the  pole  corners 
an  oblique,  or  a  double  conical,  or  a  hyperbolical  form,  as  illus- 
trated by  top  views  in  Figs.  232,  233,  and  234,  respectively. 

For  the  purpose  of  counteracting  the  magnetic  pull  due  to 
the  armature  thrust  in  bipolar  machines,  see  §  42,  the  pole- 
pieces  are  often  mounted  eccentrically,  leaving  a  smaller  gap- 
space  at  the  side  averted  from  the  field  coils  than  at  the  side 
toward  the  same,  Fig.  235,  or  in  case  of  wrought-iron  or  steel 
polepieces,  cast-iron  pole  tips  are  used  at  the  side  toward  the 
exciting  coils,  and  wrought-iron  or  steel  tips  at  the  other,  Fig. 
236.  Both  the  eccentricity  of  the  pole  faces  and  the  cast-iron  pole 
tips,  if  suitably  dimensioned,  have  the  effect  of  increasing  the 
reluctance  of  the  stronger  side  of  the  field  in  the  same  propor- 
tion as  the  density  rises  on  account  of  the  dissymmetry  of  the 
field,  thus  making  the  product  of  density  and  permeance  the 
same  in  both  halves. 

In  a  very  instructive  paper,  entitled  "On  the  Relation  of 
the  Air  Gap  and  the  Shape  of  the  Poles  to  the  Performance  of 
Dynamo-electric  Machinery,"  Professor  Harris  J.  Ryan1  has 
demonstrated  the  importance  of  making  the  polepieces  of  such 
shape  that  saturation  at  the  pole  corners  cannot  occur  even  at 
full  load;  for,  the  armature  ampere  turns  cannot  change  the 
total  magnetization  established  by  the  field  when  the  pole  cor- 
ners are  unsaturated.  He  further  proved  by  experiment  that 
for  a  sparkless  operation  at  all  loads  of  a  constant  current 

1  Transactions  A .  I.  E.  E.,  vol.  viii.  p.  451  (September  22,  1891);  Electrical 
World,  vol.  xviii.  p.  252  (October  3,  1891). 


§  77]  GENERAL    CONSTRUCTION  RULES,  299 

generator,  it  is  necessary  that  the  air  gap  be  made  of  such  a 
depth  that  the  ampere  turns  required  to  set  up  the  magnetiza- 
tion through  the  armature  without  current,  and  for  the  produc- 
tion of  the  maximum  E.  M.  F.  of  the  machine,  shall  be  a  little 
more  than  the  ampere  turns  of  the  armature  when  it  furnishes 
its  normal  current.  As  long  as  the  brushes  were  kept  under 
the  pole  faces  the  non-sparking  point  was  wherever  the  brushes 
were  placed,  no  matter  whether  the  armature  core  was  satu- 
rated or  not. 

In  order  to  enable  currents  to  be  taken  from  a  machine  at 
various  voltages,  Rankine  Kennedy1  has  proposed  to  subdivide 
the  pole  faces  by  deep,  wide  slots  parallel  to  the  armature 
shaft,  Fig.  237,  thus  providing  a  number  of  neutral  points  on 
the  commutator,  at  which  brushes  may  be  placed  without 
sparking.  If,  for  instance,  there  are  two  such  grooves  in  each 
polepiece,  the  total  voltage  of  the  machine  is  divided  into 
three  equal  parts,  and  by  employing  an  intermediate  brush  at 
one  of  the  additional  neutral  spaces,  two  circuits  can  be  sup- 
plied by  the  machine,  one  each  between  the  intermediate 
brush  and  one  of  the  main  brushes,  one  having  two-thirds  and 
the  other  one-third  of  the  total  voltage  furnished  by  the 
dynamo. 

77.  Base. 

The  base  is  the  only  part  of  the  machine  where  weight  is  not 
only  not  objectionable  but  very  beneficial,  and  it  should  there- 
fore be  a  heavy  iron  casting,  especially  as  the  extra  cost  of 
plain  cast  iron  is  insignificant  as  compared  with  the  entire  cost 
of  the  machine.  A  heavy  base  brings  the  centre  of  gravity 
low,  and  consequently  gives  great  stability  and  strength  to  the 
whole  machine. 

Besides  this  mechanical  argument  in  favor  of  a  massive  cast- 
ing, there  is  a  magnetical  reason  which  applies  to  all  types  in 
which  the  base  constitutes  a  part  of  the  magnetic  circuit,  as  is 
the  case  in  the  inverted  horseshoe  type,  Fig.  188,  in  the  ver- 
tical single-magnet  type,  Fig.  193,  in  the  inclined  and  vertical 
double-magnet  types,  Figs.  198  and  199,  respectively,  in  the 
iron-clad  types,  Figs.  203,  205,  206,  207,  218,  and  219,  respec- 
tively, and  in  the  vertical  quadruple  magnet  machine,  Fig.  224. 

1  English  Patent  No.  1640,  issued  April  4,  1892. 


300  DYNAMO-ELECTRIC  MACHINES.  [§78 

In  these  and  similar  types  a  heavy  base  of  consequent  high 
permeance  reduces  the  reluctance  of  the  entire  magnetic  cir- 
cuit, and  effects  a  saving  in  exciting  power  which  usually  is 
sufficient  to  repay  the  extra  expense  involved,  and  often  even 
reduces  the  total  cost  of  the  machine. 

If  the  base  forms  a  part  of  the  magnetic  circuit  of  the  ma- 
chine, constituting  either  the  yoke  or  one  of  the  polepieces, 
its  least  cross-section  perpendicular  to  the  flow  of  the  mag- 
netic lines  should  be  dimensioned  by  the  rules  given  for  cast- 
iron  magnets — that  is,  it  should  be  at  least  if  to  2  times  the 
area  of  the  magnet  cores,  if  the  latter  are  of  wrought  iron  or 
cast  steel,  and  at  least  of  equal  area  if  they  are  of  the  same 
material  as  the  base,  /.  e. ,  of  cast  iron. 

78.  Zinc  Blocks. 

In  some  forms  of  machines,  such  as  the  upright  horseshoe 
type,  Fig.  187,  the  horizontal  single-magnet  types,  Figs.  191 
and  192,  the  consequent  pole,  horizontal  double  magnet  type, 
Fig.  197,  the  tangential  multipolar  type,  Fig.  210,  etc.,  the 
magnet  frame  rests  upon  two  polepieces  of  opposite  polarity, 
and  if  these  were  joined  by  the  iron  base,  the  latter  would  con- 
stitute a  stray  path  of  very  much  lower  reluctance  than  the 
useful  path  through  air  gaps  and  armature,  and  the  lines  of 
force  emanating  from  these  two  polepieces  would  thus  be 
shunted  away  from  the  armature,  instead  of  forming  a  mag- 
netic field  for  the  conductors.  In  order  to  prevent  such  a 
short-circuiting  of  the  magnetic  lines  it  is  necessary  either  to 
use  material  different  from  iron  for  the  base,  or  to  interpose 
blocks  of  a  non-magnetic  substance  between  the  polepieces 
and  the  bed-plate.  The  former  method  can  be  applied  to 
small  machines  only,  and  in  this  case  the  magnet  frame  is 
mounted  upon  a  base  of  either  wood  or  brass.  For  large  ma- 
chines a  wooden  base  would  be  too  weak  and  too  light,  and  a 
brass  one  too  expensive',  and  resort  has  to  be  taken  to  the 
second  method  of  interposing  a  magnetic  insulator,  zinc  being 
most  usually  employed.  These  zinc  blocks  must  be  of  the 
necessary  strength,  not  only  to  carry  the  weight  of  the  frame, 
but  also  to  withstand  the  tremor  of  the  machine,  and  must  be 
made  high  enough  to  introduce  a  sufficient  amount  'of  reluc- 
tance into  the  path  of  leakage  through  the  base.  The  reluctance 


§78] 


GENERAL    CONSTRUCTION  RULES. 


3° * 


required  in  that  path  must  be  at  least  four  times,  and  preferably 
.should  be  up  to  ten  or  twelve  times  that  of  the  air  gaps;_that 
Is,  its  relative  permeance  calculated  from  formula  (161),  §  62, 
according  to  the  size  of  the  machine,  should  range  between  |- 
and  y1^  of  the  relative  permeance  of  the  air  gaps,  as  found  from 
formula  (167)  or  (168),  §  64,  the  amount  of  leakage  through  the 
iron  base  being  thereby  limited  to  25  per  cent,  of  the  useful 
flux  in  small  dynamos,  and  to  8  per  cent,  in  the  largest 
machines. 

This  condition  is  fulfilled  if  the  height  of  the  zinc  blocks, 
according  to  the  kind  and  the  size  of  the  machine,  is  from  three 
to  fifteen  times  greater  than  the  radial  length  of  the  gap-space. 
The  following  Tables,  LXX.,  LXXI.,  and  LXXII.,  give  the 
value  of  this  ratio,  the  consequent  height  of  the  zinc  blocks, 
and  the  corresponding  approximate  leakage  through  the  base 
for  high-speed  dynamos  with  smooth-core  drum  armatures,  for 
high-speed  dynamos  with  smooth-core  ring  armatures,  and  for 
low-speed  machines  with  toothed  and  perforated  armatures, 
respectively: 

TABLE  LXX.— HEIGHT    OF   ZINC  BLOCKS   FOB    HIGH-SPEED    DYNAMOS 
WITH  SMOOTH-CORE  DRUM  ARMATURES. 


CAPACITY 

IN 

KILOWATTS. 

Diameter 
of  Armature  Core 
.  (from  Table  X.) 

J 

£  tov 

M.53 

B«S 
£| 

-I? 

11 

«£ 

*o 

Radial  Clearance 
(from  Table  LXI.) 

Radial  Length 
of  Gap-Space. 
Inch. 

Ratio 
of  Height 
of  Zinc  Block 
to  Length  of 
Gap-Space. 

fJj 

£n  = 
5*"" 

"5 

^3 

lM 

81*5 

'§«-£ 

gUCss 

O..M  «£ 

<i«£ 

3  ° 

1 

3i" 

.3" 

.03" 

.045 

.375" 

5 

ir 

25* 

2 

8f 

.325 

.03 

.045 

.4 

5 

2 

25 

3 

4* 

.35 

.03 

.045 

.425 

5i 

2± 

25 

5 

5i 

.375 

.03 

.045 

.45 

54 

24 

20 

10 

6 

.4 

.04 

.06 

.5 

54 

2f 

20 

15 

6| 

.425 

.04 

.06 

.525 

6 

34 

18 

20 

74 

.45 

.04 

.06 

.55 

6i 

34 

18 

25 

8* 

.475 

.04 

.06 

.575 

7 

4 

16 

30 

9 

.5 

.05 

.075 

.625 

** 

44 

16 

50 

10| 

.525 

.05 

.075 

.65 

7f 

5 

15 

75 

124 

.55 

.06 

.09 

.7 

84 

6 

14 

100 

15 

.6 

.06 

.09 

.75 

8f 

64 

14 

150 

184 

.65 

.065 

.125 

.84 

9 

74 

12 

200 

224 

.7 

.07 

.16 

.93 

9f 

9 

10 

300 

28 

.8 

.07 

.19 

1.06 

104 

11 

10 

302 


DYNAMO-ELECTRIC  MACHINES. 


[§78 


TABLE  LXXI.— HEIGHT  OF    ZINC  BLOCKS  FOR  HIGH-SPEED  DYNAMOS 
WITH  SMOOTH-CORE  RING  ARMATURES. 


fc$ 

^ 

*§ 

CAPACITY 

IN 

KILOWATTS. 

Diameter 
of  Armature  Co 
(from  Table  XI 

1 

if 

o 

Radial  Clearaix 
I  (from  Table  LX 

Radial  Lengtl 
of  Gap-Space, 
Inch. 

H 

"o-" 

J, 

f|| 

Approximate 
1  Leakage  throng 
Base  in  p.  c. 
of  Useful  Fluj 

1 
2 

7" 
8 

.25" 
.25 

.03" 
.03 

.045" 
.045 

.325" 
.325 

9 

3 

15* 

14 

3 

94 

.275 

.04 

.06 

.375 

94 

34 

14 

5 

11 

.3 

.04 

.C6 

.4 

10 

4 

12 

10 

14 

.325 

.05 

.075 

.45 

11 

5 

12 

15 

15 

.325 

.05 

.075 

.45 

11 

5 

12 

20 

16 

.35 

.06 

.09 

.5 

12 

6 

10 

25 

18 

.35 

.06 

.09 

.5 

12 

6 

10 

30 

20 

.375 

.07 

.13 

.575 

12 

7 

10 

50 

24 

.4 

.07 

.13 

.6 

134 

8 

9 

75 

28 

.425 

.07 

.155 

.65 

144 

94 

9 

100 

32 

.45 

.07 

.155 

.675 

154 

104 

8 

150 

36 

.475 

.07 

.18 

.725 

16 

114 

8 

TABLE  LXXII.— HEIGHT  OF  ZINC  BLOCKS  FOR  LOW-SPEED  DYNAMOS 
WITH  TOOTHED  AND  PERFORATED  ARMATURE. 




^— 

0) 

M 

Q)  '""^ 

Q)  —  ' 

O>      • 

•as 

^P-I 

CAPACITY 

IN 

KILOWATTS. 

Diameter 
of  Armature  Coi 
(from  Table  XII 

Height 
of  Winding  Spac 
(from  Table  XVIJ 

Radial  Clearanc 
(from  Table  LXJ 

Maximum  Radi 
Length  of  Gap-Sp 
Inch. 

Ratio 
of  Height 
of  Zinc  Block 
to  Maximum  Len 
of  Gap-Space. 

I 

N1"1 
"o 

If  S 

2 

12" 

H" 

•   • 

H" 

3 

34" 

15^ 

3 

15 

li 

1 

5 

3 

4 

15 

5 

17 

If 

TS 

JJ| 

34 

5 

12 

10 

21 

14 

5 

^T 

3f 

6 

12 

15 

23 

If 

tt 

II 

4 

6f 

10 

20 

25 

Hi 

TS 

Iff 

4i 

74 

10 

25 

27 

if 

3 

IST. 

8 

10 

30 
50 

30 
36 

it* 

4 
4 

S" 

4f 

8f 
94 

8 
8 

From  the  comparison  of  the  above  Tables  LXX.,  LXXI.  and 
LXXII.,  it  follows  that  the  height  of  the  zinc  blocks  increases 
in  a  nearly  direct  proportion  with  the  diameter  of  the  armature 


§79] 


GENERAL    CONSTRUCTION  RULES. 


core,  and  that,  for  the  same  armature  diameter,  a  smooth- 
drum  machine  requires  a  higher,  and  a  toothed  or  perforated 
armature  machine  a  lower  zinc  than  a  smooth-ring  dynamo. 
By  compiling  the  results  of  Tables  LXX.,  LXXL,  and  LXXIL, 
the  following  Table,  LXXIII.,  is  obtained,  from  which  it  can  be 
seen  that  the  heights  of  zinc  blocks  for  smooth-ring  machines 
are  from  18  to  30  per  cent,  less  than  for  smooth-drum  dyna- 
mos, and  those  for  machines  with  toothed  and  perforated 
armatures  are  from  n  to  20  per  cent,  less  than  for  smooth-ring: 
armature  dynamos: 

TABLE  LXXIII. — COMPARISON   OP   ZINC   BLOCKS  FOR   DYNAMOS   WITH 
VARIOUS  KINDS  OF  ARMATURE. 


HEIGHT  OF  ZINC  BLOCKS. 

DIAMETER 

OF 

Smooth  Armature. 

Toothed 

ARMATURE  CORE. 

or 
Perforated 

Drum. 

Ring. 

Armature. 

Inches. 

Inches. 

Inches. 

Inches. 

3 

If 

4 

2 

6 

2f 

2 

14 

8 

4 

3 

ft 

10 

5 

3i 

3 

12 

5f 

4i 

31 

15 

G* 

5 

4 

18 

7i 

6 

5 

21 

8f- 

7 

6 

24 

9f 

8 

7 

27 

11 

9 

8 

30 

.  . 

10 

84 

36 

•• 

Hi 

H 

79.  Pedestals  and  Bearings. 

In  the  design  of  the  base,  especially  when  the  portion  of  the 
field  frame  above  the  armature  centre  cannot  be  lifted  off,  care 
should  be  taken  that  the  armature  can  easily  be  withdrawn 
longitudinally  by  removing  one  of  the  bearing  pedestals, 
which,  therefore,  should  be  a  separate  casting.  In  machines 
where  the  lowest  point  of  the  armature  periphery  is  at  a  con- 
siderable height  above  the  base,  as  for  instance  in  dynamos  of 


304  DYNAMO-ELECTRIC  MACHINES.  [§79 

the  overtypes,  Figs.  188,  191,  198,  and  206,  respectively,  fur- 
ther of  the  vertical  double  types,  Figs.  197,  202,  207,  219,  and 
224,  respectively,  and  of  the  radial  and  tangential  outerpole 
types,  Figs.  208  and  210,  respectively,  it  is  preferable  that  the 
pedestals  should  be  made  of  two  parts,  the  upper  part,  which 
should  have  a  depth  from  the  shaft  centre  a  little  in  excess  of 
the  radius  of  the  finished  armature,  being  removable,  while  the 
lower  portion,  which  may  be  cast  in  one  with  the  base,  will 
form  a  convenient  resting  place  for  the  armature  in  removal. 

In  most  cases  this  problem  of  making  high  pedestals  of  two 
parts  can  practically  be  solved  by  boring  out  the  pedestal  seats 
together  with  the  polepieces,  thus  providing  a  cylindrical  seat 
for  the  pillow  blocks,  as  shown  in  Fig.  238.  This  design  is 
particularly  advantageous  also  for  machines  in  which  the  base 
forms  one  of  the  polepieces,  as  for  example,  the  forms  shown 
in  Figs.  193,  199  and  219,  as  in  this  case,  outside  of  the  finish- 
ing of  the  core  seats,  this  boring  to  a  uniform  radius  is  the 
only  tooling  necessary  for  the  base. 

If  the  field  frame  is  symmetrical  with  reference  to  the  hori- 
zontal plane  through  the  armature  centre,  the  frame  of  the 
machine  is  usually  made  in  halves,  and  the  armature,  in  case 
of  repair,  can  be  removed  by  lifting  it  from  its  bed  without 
disturbing  the  bearing  pedestals.  The  bearing  boxes  must  for 
this  purpose  be  made  divided  so  that  all  parts  of  the  machine 
above  the  shaft  centre  are  removable.  This  design  affords  the 
further  advantage  that  the  bearing  caps  can  be  taken  off  at 
any  time  and  the  bearings  inspected,  and  it  has  for  this  reason 
become  a  general  practice  in  dynamo  design  to  employ  split 
bearings,  even  for  types  in  which  the  armature  cannot  be  lifted. 

It  is,  further,  of  great  importance  that  the  bearing  should 
not  only  be  exactly  concentric,  but  that  they  also  should  be 
accurately  in  line  with  each  other;  for  large  machines  it  is 
therefore  advisable  to  effect  automatic  alignment  by  providing 
the  bearings  with  spherical  seats.  This  can  be  attained  either 
by  giving  the  enlarged  central  portion  of  the  shell  a  spherical 
shape,  Fig.  239,  or  in  providing  the  bottom  part  of  the  box 
with  a  spherical  extension  fitting  into  a  spherical  recess  in  the 
pedestal,  Fig.  240. 

In  order  to  prevent  heating  of  the  bearings,  the  shells  in 
modern  dynamos  are  usually  furnished  with  some  automatic 


§80] 


GENERAL    CONSTRUCTION  RULES. 


3°5 


oiling  device,  the  most  common  form  of  which,  shown  in  Fig. 
241,  consists  of  a  brass  ring  or  chain  dipping  into^  the  oil 
chamber  of  the  box  and  resting  upon  and  turning  with  the 
shaft,  thereby  causing  a  continuous  supply  of  oil  at  the  top  of 
the  shaft.  A  further  improvement  of  this  self-oiling  arrange- 
ment, patented  in  1888  by  the  Edison  General  Electric  Com- 
pany, is  illustrated  in  Fig.  242.  In  this  the  interior  of  the 


FIG.  238 


FIG.  239 


FIQ.  240 


SECTION  C-D 


FIQ.  242 

Figs.  238  to  242. — Pedestals  and  Bearings. 

shell  is  provided  with  spiral  grooves  filled  with  soft  metal  and 
forming  channels  for  conveying  oil  from  each  end  of  the  bear- 
ing to  a  circumferential  groove  which  surrounds  the  shaft  at 
the  centre  of  the  shell,  and  which  communicates  with  the  oil 
chamber  beneath  the  bearing.  These  grooves  not  only  effect 
a  steady  supply,  but  a  continuous  circulation  of  oil,  the  latter 
being  lifted  from  the  reservoir  into  the  shell  by  the  oiling 
rings,  thence  forced  by  the  spiral  channels  into  the  central 
groove,  from  where  it  flows  back  into  the  oil  chamber. 

80.  Joints  in  Field  Magnet  Frame. 

a.   Joints  in  Frames  of  One  Material. 

Magnet  frames  consisting  of  but  one  material  may  either  be 
formed  of  one  single  piece  or  may  be  composed  of  several 
parts.  If  the  frame  is  of  cast  iron  or  cast  steel,  in  small 


DYNAMO-ELECTRIC  MACHINES.  [§80 

dynamos  usually  the  former  is  the  case,  /.  e.,  the  whole  frame 
is  cast  in  one,  while  in  large  machines  it  generally  consists  of 
two  castings;  if,  however,  wrought  iron  is  used,  it  is,  as  a 
rule,  much  more  convenient  to  forge  each  part  separately  and 
to  build  up  the  frame  by  butt-jointing  the  parts.  In  so  joint- 
ing a  magnet  frame,  it  is  of  the  utmost  importance  to  accu- 
rately adjust  and  finish  the  surfaces  to  be  united,  so  as  to  make 
'the  joint  as  perfect  as  possible,  for  every  poorly  fitted  joint, 
by  reduction  of  the  sectional  area  at  that  point,  introduces  a 
considerable  reluctance  in  the  magnetic  circuit.  If,  however, 
the  contact  between  the  two  surfaces  is  as  good  as  planing  and 
scraping  can  make  it,  a  practically  perfect  joint  is  obtained, 
and  the  additional  reluctance,  which  then  only  depends  upon 
the  degree  of  magnetization,  is  entirely  inappreciable  for  such 
high  magnetic  densities  as  are  employed  in  modern  dynamos. 
Experiments  have  shown  that  at  low  densities  the  additional 
magnetomotive  force  required  to  overcome  the  reluctance  of 
a  joint  is  very  much  greater,  comparatively,  than  at  high  in- 
ductions, which  is  undoubtedly  due  to  the  pressure  created  by 
the  magnetic  attraction  of  the  two  surfaces  across  the  joint, 
this  pressure  being  proportional  to  the  square  of  the  density. 
The  following  Table  LXXIV.  shows  the  influence  of  the  den- 
sity of  magnetization  upon  the  effect  of  a  well-fitted  joint  in  a 
wrought  iron  magnet  frame,  the  induction  in  the  iron  ranging 
from  10,000  to  120,000  lines  per  square  inch,  and  indicates 
that  the  reluctance  of  the  joint  becomes  the  less  significant  the 
nearer  saturation  of  the  iron  is  approached. 

At  a  magnetic  density  of  &"m=  10,000  lines  of  force  per 
square  inch,  each  joint  in  the  circuit  is  equivalent  to  an  air 
space  of  .0016  inch,  or  has  a  reluctance  equal  to  that  of  an 
additional  length  of  3  inches  of  wrought  iron;  at  (B*m=  100,000 
lines  per  square  inch,  the  thickness  of  an  equivalent  air  space 
is  only  .00065  inch,  which  corresponds  to  the  reluctance  of 
.22  inch  of  wrought  iron  at  that  density;  and  at  or  above  (B"m 
=  120,000,  finally,  a  good  joint  is  found  to  have  no  effect 
whatever  upon  the  reluctance  of  the  circuit. 

b.   Joints  in  Combination  Frames. 

For  magnet  frames  consisting  of  two  or  three  different  mate- 
rials the  same  rule  as  for  frames  of  one  material  holds  good  as 


80] 


GENERAL    CONSTRUCTION  RULES. 


307 


to  the  nature  of  the  joint,  but  since  the  ordinary  butt-jointing 
would  limit  the  capacity  of  the  joint  to  that  of  the  inferior 
magnetic  material,  it  is  essential  in  the  case  of  combination 
frames  to  increase  the  area  of  contact  in  the  proportion  of  the 
relative  permeabilities  of  the  two  materials  joined.  Thus,  if 
wrought  and  cast  iron  are  butt-jointed,  the  capacity  of  the 
joint  is  reduced  to  that  of  the  cast  iron,  whereby  the  advantage 
of  the  high  permeability  of  the  wrought  iron  is  destroyed  and 
the  permeance  of  the  circuit  is  considerably  increased;  and  in 
order  to  have  the  full  benefit  of  the  wrought  iron,  the  contact 
area  of  the  joint  must  be  increased  proportionally  to  the  ratia 
of  the  permeability  of  the  wrought  iron  to  that  of  the  cast  iron 
at  the  particular  density  employed. 

TABLE  LXXIV. — INFLUENCE  OP  MAGNETIC  DENSITY  UPON  THE  EFFECT 
OF  JOINTS  IN  WROUGHT  IRON. 


PRESSURE 
ON  JOINT 

MAGNETIZING  FORCE 
REQUIRED  FOR  1  INCH. 

DIFFER- 

EQUIVALENT OF  JOINT- 

DENSITY  or 
MAGNET- 
IZATION. 

DUE    TO 

MAGNETIC 
ATTRAC- 

ENCE 

DUE  TO 

JOINT, 

Air  Space, 

Length  of 
Iron, 

&"m 

TION. 
/nff     2 

Solid. 

Jointed. 

5C—  - 

OC 

OC 

T 

Lines 
per  sq.  in. 

®  m 

3C, 

Amp. 

5 

Amp. 

,TC         .1C 

72,134,000 

uv2         "^i 
Amp. 

.3133  X  &"m 

36 

Ibs. 

turns. 

turns. 

turns. 

Inch. 

Inch. 

per.  sq.  in. 

i 

10,000 

1.4 

1.7 

6.7 

5 

.0016 

3.0 

20,000 

5.5 

3.2 

12.6 

9.4 

.00155 

2.9 

30,000 

12.5 

5 

19.1 

14.1 

.0015 

2.8 

40,000 

22 

7 

25.2 

18.2 

.00145 

2.6 

50,000 

35 

9.5 

31.4 

21.9 

.0014 

2.3 

60,000 

50 

12.7 

38.1 

25.4 

.00135 

2.0 

70,000 

68 

18.3 

45.7 

27.4 

.00125 

1.5 

80,000 

89 

27.6 

55.2 

27.6 

.0011 

1.0 

90,000 

112 

50.8 

76.2 

25.4 

.0009 

0.5 

95,000 

125 

68 

91.8 

23.8 

.0008 

.35 

100,000 

139 

90 

110 

20 

.00065 

.22 

105,000 

153 

134 

150 

16 

.0005 

.12 

110,000 

168 

288 

300 

12 

.00035 

.04 

112,500 

176 

391 

400 

9 

.00025 

.023 

115,000 

183 

500 

506 

6 

.00016 

.012 

117,500 

192 

600 

603 

3 

.00008 

.005 

120,000 

200 

700 

700 

0 

.00000 

.000 

For  a  density  in  wrought  iron  of  100,000  lines  of  force  per 
square  inch,  for  example,  a  magnetomotive  force  of  90  ampere- 
turns  is  required  per  inch  length  of  the  circuit,  and  the  same 


308 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§80 


specific  magnetomotive  force  is  capable  of  setting  up  about 
40,000  lines  per  square  inch  in  cast  iron;  the  contact  area  of  a 
joint  between  wrought  iron  and  cast  iron  in  this  case  must 
therefore  be  increased  in  the  ratio  of  100,000  :  40,000,  or  must 
be  made  2\  times  the  cross-section  of  the  wrought  iron  in 
order  to  reduce  the  permeability  of  the  joint  to  that  of  the 
wrought  iron. 

In  practice  this  problem  of  providing  a  sufficiently  large  con- 
tact area  between  a  wrought  and  a  cast  iron  part  of  the  mag- 

FlQ.243  FiQ.,244  FI3.245  FlQ.  246 


FlQ.  247 


FIG  248 


FlQ.  249 


FlQ  250 


.W.I. 
'STUD 


Figs.  243  to  250. — Joints  in  Magnetic  Circuits. 

netic  circuit  may  be  solved  either  by  setting  the  wrought  iron 
into  the  cast  iron,  or  by  extending  the  surface  of  the  wrought 
iron  part  near  the  joint  by  means  of  flanges;  or,  finally,  by  in- 
serting an  intermediate  wrought-iron  plate  into  the  joint.  In 
Figs.  243,  244,  245  and  246  are  shown  four  methods  of  increasing 
the  area  of  the  joint  by  means  of  projecting-  the  wrought-iron 
core  into  the  cast-iron  yoke  or  polepiece,  differing  only  in  the 
manner  of  securing  a  good  contact  between  the  parts,  the  first 
one  employing  a  set-screw,  the  second  one  a  wrought-iron  nut, 
and  the  third  one  using  a  conical  fit  with  draw-screw  for  this 
purpose,  while  in  the  fourth  one  the  threaded  projection  of  the 
core  itself  forms  the  tightening  screw.  Fig.  247  illustrates  a 
modification  of  the  method  shown  in  Fig.  246,  a  separate  screw- 
stud  being  used  instead  of  the  threaded  extension  of  the 
wrought-iron  core.  In  case  of  rectangular  magnet  cores  the 
arrangement  shown  by  plan  in  Fig.  248  effects  an  excellent 


§  80]  GENERAL    CONSTRUCTION  RULES.  3°9 

joint;  in  this  the  cores  are  inserted  into  the  base  from  the  sides, 
thus  offering  three  surfaces  to  form  the  contact  area. -The 
manner  of  supplying  the  necessary  joint  surface  by  flanged  ex- 
tensions of  the  wrought-iron  core  is  illustrated  in  Fig.  249, 
which  shows  the  method  of  fastening  employed  in  large  multi- 
polar  machines,  feather-keys  being  used  to  secure  exact  rela- 
tive position  of  the  cores.  In  Fig.  250,  finally,  a  joint  is  shown 
in  which  a  wrought-iron  contact  plate  is  inserted  between  the 
wrought-iron  core  and  the  cast-iron  yoke  or  polepiece  with 
the  object  of  increasing  the  area  of  the  joint  and  of  spreading 
the  lines  of  force  gradually  from  the  smaller  area  of  the 
wrought  iron  to  the  larger  of  the  cast  iron. 


CHAPTER  XVI. 

CALCULATION    OF    FIELD    MAGNET    FRAME. 

81.  Permeability  of  the  Various  Kinds  of  Iron.— Ab- 
solute and  Practical  Limits  of  Magnetization. 

The  field  magnet  of  a  dynamo  has  the  function  of  supplying 
to  the  interpolar  space  in  which  the  armature  conductors  revolve 
magnetic  lines  of  force  in  a  number  sufficient  either  to  cause 
the  generation  of  the  required  electromotive  force,  in  case  of 
a  generator,  or  to  produce  a  motion  of  the  desired  power,  in 
•case  of  a  motor.  The  cross-sections  of  the  various  parts  of 
the  field  magnet  frame,  that  is,  of  the  iron  structure  consti- 
tuting the  path  or  paths,  for  the  flow  of  these  magnetic  lines, 
consequently,  must  be  dimensioned  with  reference  to  the  num- 
ber of  lines  of  force  to  be  carried,  and  to  the  magnetic  con- 
ductivity of  the  material  used. 

The  number  of  lines  which  by  a  certain  exciting  power  or 
magnetomotive  force  can  be  passed  through  a  portion  of  a 
magnetic  circuit  depends  upon  the  area  of  the  cross-section 
and  on  the  magnetic  conductivity  of  the  material  of  that  part 
of  the  circuit.  The  various  magnetic  materials,  according 
to  their  hardness,  have  a  different  capability  of  conducting 
magnetic  lines,  the  softest  material  being  the  best  magnetic 
conductor.  The  specific  magnetic  conductance  of  air  being 
taken  as  unity,  the  relative  magnetic  conductance,  or  the  rela- 
tive permeance,  of  the  various  magnetic  materials  is  indicated 
by  the  ratio  of  the  number  of  lines  of  force  produced  in  unit 
cross-section  of  these  materials  to  the  number  of  lines  set  up 
by  the  same  magnetizing  force  in  unit  cross-sections  of  air. 
This  ratio,  or  coefficient  of  magnetic  induction,  is  called  the 
magnetic  conductivity,  or  \h.t  permeability  of  the  material. 

The  number  of  lines  per  square  centimetre  of  sectional  area 
set  up  by  a  certain  magnetizing  force  in  air  is  conventionally 
designated  by  X,  that  in  iron  by  (B,  and  the  permeability  by 


§81] 


CALCULATION  OF  FIELD  MAGNET  FRAME. 


the   symbol    /^  ;    between    these   three    quantities,    therefore, 
exists  the  relation 


=  w,  or  (E  =  yu  X  OC 


(215) 


Since  for  air  the  permeability  j.i  =  i,  the  number  of  lines  of 
force  per  square  centimetre  of  air  is  numerically  equal  to  the 
magnetizing  force  in  magnetic  measure,  /.  e.,  in  current-turns. 
Permeability  is  therefore  often  also  defined  as  the  ratio  of  the 
magnetization  produced  to  the  magnetizing  force  producing  it. 

TABLE  LXXV. — PERMEABILITY  OF  DIFFERENT  KINDS  OF  IRON  AT  VAR- 
IOUS MAGNETIZATIONS. 


DENSITY  OP 
MAGNETIZATION. 


PERMEABILITY,  /u,. 


Lines 
per  sq.  inch 
•<$>" 

Lines 
per  cm'. 

(B 

Annealed 
Wrought 
Iron. 

Commercial 
Wrought 
Iron. 

Gray 
Cast 
Iron. 

Ordinary 
Cast 
.  Iron. 

20,000 

3,100 

2,600 

1,800 

850 

650 

25,000 

3,875 

2,900 

2,000 

800 

700 

30,000 

4,650 

3,000 

2,100 

600 

770 

35,000 

5,425 

2,950 

2,150 

400 

800 

40,000 

6,200 

2,900 

2,130 

250 

770 

45,000 

6,975 

2,800 

2,100 

140 

730 

50,000 

7,750 

2,650 

2,050 

110 

700 

55,000 

8,525 

2,500 

1,980 

90 

600 

60,000 

9,300 

2,300 

1,850 

70 

500 

65,000 

10,100 

2,100 

1,700 

50 

450 

70,000 

10,850 

1,800 

1,550 

35 

350 

75,000 

11,650 

1,500 

1,400 

25 

250 

80,000 

12,400 

1,200 

1,250 

20 

200 

85,000 

13,200 

1,000 

1,100 

15 

150 

90,000 

14,000 

800 

900 

12 

100 

95,000 

14,750 

530 

680 

10 

70 

100,000 

15,500 

360 

500 

9 

50 

105,000 

16,300 

260 

360 

. 

.... 

110,000 

17,400 

180 

260 

, 

.... 

115,000 

17,800 

120 

190 

120,000 

18,600 

80 

150 

125,000 

19,400 

50 

120 

f 

130,000 

20,150 

30 

100 

. 

.  .  ,  . 

135,000 

20,900 

20 

85 

. 

140,000 

21,700 

15 

75 

•    • 



While  the  permeability  of  air  and  of  all  non-magnetic  sub- 
stances is  a  constant  (for  air  it  is  i,  and  for  diamagnetic  mate- 
rials slightly  less  than  i)  for  all  stages  of  magnetization,  that 
of  magnetic  materials  varies  with  the  degree  of  saturation. 


3  *  2  D  YNA  MO-ELEC TRIG  MA  CHINES.  [§  8 1 

The  more  lines  a  certain  cross-section  of  iron  carries,  the  less 
permeable  is  it  for  additional  lines,  as  is  evident  from  the 
preceding  Table  LXXV.  containing  the  average  permeabilities 
of  different  kinds  of  iron  at  various  degrees  of  magnetization. 
At  a  certain  limit,  for  every  kind  of  iron,  a  very  material  in- 
crease in  the  magnetizing  forces  does  not  appreciably  increase 
the  magnetization  induced,  and  the  iron  is  then  saturated 
with  lines  of  force.  This  limit  of  magnetization  in  annealed 
wrought  iron  is  reached  at  a  density  of  about  (&"=  130,000  lines 
per  square  inch,  or  (B  =  20,200  lines  per  square  centimetre; 
in  soft  steel  at  (&"=  127,500  lines  per  square  inch,  or  (B  =  19, Sea- 
lines  per  square  centimetre;  in  mitis  iron  at  ($>"=  122,500  lines 
per  square  inch,  or  (B  =  19,000  lines  per  square  centimetre;  in 
cast  iron  with  a  6.5  per  cent,  admixture  of  aluminum  at  (B"  = 
87,500  lines  per  square  inch,  or  OJ  =  13,500  lines  per  square 
centimetre,  and  in  ordinary  cast  iron  at  (&"=  77,500  lines  per 
square  inch,  or  (B  —  12,000  lines  per  square  centimetre  of  cross- 
section.  The  magnetizations,  however,  to  which  these  mate- 
rials are  subjected  in  practical  electromagnets  are  taken  far 
below  the  actual  limits  of  absolute  saturation,  since  "saturation 
curves"  indicating  the  variation  of  the  induction  (B,  with  in- 
creasing magnetizing  force,  X,  show  that  from  a  certain  point, 
the  "knee"  of  the  curve,  the  magnetization  increases  much 
slower  than  the  magnetizing  force  which  causes  it.  In  wrought 
iron,  for  instance,  an  induction  of  (B  =  13,580  requires  a  mag- 
netizing force  of  5C  =  25,  an  induction  of  (B  =  16,000  a  magneto- 
motive force  of  3C  =  50,  and  density  of  (B  =  16,500  necessitates- 
an  exciting  power  of  X  =100;  and  an  increase  of  100  per  cent, 
in  the  magnetizing  force,  consequently  causes  a  rise  in  density 
of  i8j^  per  cent,  at  the  lower  magnetization,  while  again 
doubling  the  magnetomotive  force  at  the  higher  induction  only 
causes  an  increase  in  magnetic  density  of  about  3  per  cent. 
In  practice,  therefore,  t.he  limits  of  the  magnetic  densities  of 
the  different  materials  are  to  be  fixed  with  regard  to  the  rela- 
tive economy  of  iron  and  copper.  Taking  the  practical  limit 
of  saturation  too  low  means  a  small  saving  of  copper  at  a  large 
expense  of  iron,  while  too  high  a  density  effects  a  compara- 
tively small  saving  of  iron  at  a  large  expense  of  copper.  Since 
copper  costs  many  times  more  than  iron,  the  densities  should 
be  limited  rather  low,  the  tendency  toward  the  former  extreme 


§82]         CALCULATION  OF  FIELD  MAGNET  FRAME.          313 

being  preferable  to  that  toward  the  latter.  With  this  point 
in  view,  the  "  Practical  Working  Densities  "  given  in  the  follow- 
ing Table  LXXVI.  are  recommended  for  use  in  dynamo 
designing,  while  under  the  heading  of  '•'•Practical  Limits  of 
Magnetization"  the  highest  densities  are  tabulated  that  the 
author  would  advise  to  allow  in  magnet  frames  of  dynamo- 
electric  machines.  For  sake  of  completeness  the  "Absolute 
Saturation  "  of  the  various  materials,  as  given  above,  are  added 
in  Table  LXXVI.  : 


TABLE  LXXVI. — PRACTICAL  WORKING  DENSITIES  AND  LIMITS  OF  MAG- 
NETIZATION FOR  VARIOUS  MATERIALS. 


MATERIAL. 

PRACTICAL 
WORKING  DENSITY. 

PRACTICAL  LIMIT 
OP  MAGNETIZATION. 

ABSOLUTE 
SATURATION. 

Lines  p. 
sq.  inch. 

<B"m 

Lines  p. 
sq.  cm. 

&m 

Lines  p. 
sq.  inch. 

Lines  p. 
sq.  cm. 

Lines  p. 
sq.  inch. 

Lines  p. 
sq.  cm. 

Wrought  Iron  

90,000 
85,000 
80,000 

45,000 
40,000 

14.000 
13,200 
12,400 

7,000 
6,200 

105,000 
100,000 
95,000 

55,000 
50,000 

16,300 
15,500 
14,750 

8,500 

7,750 

130,000 
127,500 
122,500 

87,500 
77,500 

20,200 
19,800 
19,000 

13,500 
12.000 

Cast  Steel  

Mitislron  

Cast  Iron,  containing 
6.5%  Aluminum  
Cast  Iron,  ordinary  ... 

82.  Sectional  Area  of  Magnet  Frame. 

The  magnet  frame  carries  the  total  flux  generated  in  the 
machine;  according  to  §  81,  consequently,  the  cross  section  of 
any  portion  of  it  must  be 


o//    _ 

O     m    


or 


(ft 


(216) 


S"    = 


A,    = 


Area  of  magnet  frame,  in  square  inches; 

Total  flux  generated  in  machine,  from  formula 

(156),  §60; 
Useful  flux  necessary  to  produce  the  required 

E.  M.  F.,  from  formula  (137),  §56; 
Factor  of  magnetic  leakage,   preliminary    value 

from  Table  LXVIII.,  §70,  final  value  from  for- 

mula (157),  §  61; 
Magnetic  density  in  magnet  frame,   from  Table 

LXXVI.,  §81. 


3 H  DYNAMO-ELECTRIC  MACHINES.  [§82 

If  only  one  material  is  used  the  value  found  from  formula 
(216)  is  the  uniform  cross-section  of  the  whole -frame,  /.  e.,  of 
the  cores,  the  yoke,  and  the  polepieces;  in  case  of  combina- 
tion frames,  however,  the  area  for  each  material  must  be 
calculated  separately: 

For  Wrought  iron,         S"m  =  — — ;     (217) 


i  ( 


Cast  steel, 


Mitis  iron,  S*m  =  ~^;     (219) 

80,000 ' 

Cast    iron,    con- 
taining 6. 5$  _  A.   x  # 

of  aluminum,      S"m  —  -        —\      • (220) 

45,000 

Ordinary  cast  A   X  ^ 

iron,  S'"m  =  - 


In  combining  the  averages  for  the  useful  flux,  taken  from 
Table  LXIV.,  §  59,  for  the  practical  conductor  velocities  given 
in  Tables  X.,  XI.  and  XII.,  respectively,  with  the  leakage 
coefficients  compiled  in  Table  LXVIIL,  §  70,  the  average  total 
flux,  0,  for  dynamos  of  various  kinds  and  sizes  is  obtained, 
and,  then  by  applying  formulae  (217)  to  (221),  the  sectional  areas 
of  the  field  frame  for  various  kinds  and  sizes  of  machines  can 
be  found.  In  this  manner  the  following  Tables  LXXVIL, 
LXXVIII.,  and  LXXIX.,  have  been  prepared,  which  give  the 
cross-sections  of  field  magnet  frames  of  different  materials  for 
high-speed  drum  machines,  high-speed  ring  dynamos,  and  low 
speed  ring  machines,  respectively. 

The  figures  given  for  the  areas  directly  apply  to  single 
circuit  bipolar  dynamos  only;  for  double  circuit  bipolar,  and 
for  multipolar  machines  they  represent  the  total  cross-section 
of  all  the  magnetic  circuits  in  parallel,  or  for  frames  of  only 
one  material,  the  total  area  of  all  the  cores  of  same  free 
polarity,  the  cross-sections  of  the  various  portions  of  the  field 
magnet  frame  are  therefore  obtained  in  dividing  these  figures 
by  the  number  of  magnetic  circuits,  /.  e.,  by  the  number  of 
pairs  of  magnet  poles: 


§82] 


CALCULATION  OF  FIELD  MAGNET  FRAME. 


315 


TABLE    LXXVII.— SECTIONAL  AREA   OF  FIELD   MAGNET  FRAME  FOR 
HIGH-SPEED  DRUM  DYNAMOS. 


5 

AREA  OF  FIELD  MAGNET  FRAME. 

§  .i 

Average 

, 

&    | 

Useful 

Fln-v 

Av  age 
Leak'ge 

Average 
total 

Cast 

Cast 

"o     "* 

I  j 

0  1 

1'  1UX. 

Table 
LXIV. 
Lines  of 
force. 

Coeffi- 
cient. 
Table 
LXVIII 

flux, 
<&'. 
Lines  of 
force. 

Wr'ght 
Iron, 
Sm 

Cast 
Steel, 
Sm 

Mitis 
Iron, 
Sm 

Iron, 
6.5*  Al. 
Dm 

Iron, 
ordin'y 
Sm 

s 

y 

90,000 

~  85,000 

80,000 

45,000 

40,000 

sq.  in. 

eq.  in. 

q.  in. 

sq.  in. 

sq.  in. 

.1 

25 

200,000 

2.00 

400,000 

4.5 

4.7 

5 

9 

10 

.25 

30 

333,000 

1.90 

630,000 

7 

7.4 

7.9 

14 

15.8 

.5 

32 

550,000 

1.80 

990,000 

11 

11.7 

12.4 

22 

24.8 

1 

34 

880,000 

1.75 

I,640,0c0 

17.1 

18.1 

193 

34.2 

38.6 

2 

36 

1,530,000 

1.70 

2,600,000 

289 

30.b 

32.5 

57.8 

65 

3 

40 

1,875,000 

1.65 

3,100,000 

34.5 

36.5 

38.8 

69 

77.6 

5 

45 

2,550,000 

1.60 

4,080,000 

45.5 

48 

51 

91 

102 

10 

50 

4.000,000 

1.55 

6,200,000 

69 

73 

77.5 

138 

155 

15 

50 

5,700,000 

1.50 

8,550,000 

95 

101 

107 

190 

214 

20 

50 

7,200,000 

1.45 

10,400.000 

115.5 

122 

130 

231 

260 

25 

50 

8,500,000 

1.40 

11,900,000 

132 

140 

149 

264 

298 

30 

50 

9,900,000 

1.40 

13,850,000 

154 

163 

173 

SOS 

346 

50 

50 

15,500,000 

1.35 

20,900,000 

232 

246 

261 

464 

522 

75 

50 

22,000,000 

1.35 

29,700,000 

330 

350 

371 

660 

742 

100 

50 

28.000,000 

1.30 

36,400,000 

405 

430 

455 

810 

910 

150 

50 

39,500,000 

1.30 

51,400,000 

572 

605 

643 

1,144 

1,286 

200 

50 

50,000,000 

1.25 

62,500.000 

695 

735 

782 

1,390 

1,564 

300 

50 

70.000.000 

1.20 

84,000,000 

933 

990 

1,050 

1,866 

2,100 

TABLE  LXXVIII. — SECTIONAL  AREA  OF  FIELD  MAGNET  FRAME  FOR 
HIGH-SPEED  RING  DYNAMOS. 


>• 

AREA  OF  FIELD  MAGNET  FRAME. 

Capacity 
in 
Kilowatts. 

iductor  Veloc 
(Table  Xtt. 
't.  per  second 

Average 
Useful 
Flux. 
(Table 
LXIV.) 
Lines  of 
force. 

Av'age 
Leak'ge 
Coeffi- 
cient. 
Table 
LXVIII 

Average 
Total 
Flux, 

Lines  of 
force. 

Wr'ght 
Iron, 
8m 

Cast 
Steel, 
Sm 

Mitis 
Iron, 
Sm/ 

Cast 
Iron, 
6.5*  Al. 
Sm 

Cast 
Iron, 
ordm'y 

3  ' 

~  90,000 

85,000 

80,000 

45,000 

~  40,000 

eq.  in. 

sq.  in. 

sq   in. 

sq.  in. 

sq.  in. 

.1 

50 

100,000 

1.80 

180,000 

2 

2.1 

2.2 

4 

4.5 

.25 

55 

182,000 

1.70 

310.000 

3.5 

3.7 

3.9 

7 

7.8 

.5 

60 

292,000 

1.60 

467,000 

5.2 

5.5 

5.8 

10.4 

11.6 

1. 

65 

462.000 

1.55 

715,000 

8 

8.4 

8.9 

16 

17.8 

2.5 

70 

930,000 

1.50 

1,400.000 

15.5 

16.5 

17.5 

31 

35 

5 

75 

1.500,000  i     1.45          2,180,000 

24.2 

25.6 

27.3 

48.4 

54.5 

10 

80 

2,500,000 

1.40     !      3.500,000 

39 

41.2 

43.8 

78 

87.5 

25 

80 

5,320,000 

1.35 

7,200,000 

80 

85 

90 

160 

180 

50 

85 

9,120,000 

1.30 

11,900,000 

132 

140 

149 

264 

298 

75 

85 

13,000,000 

1.25 

16,250,000 

180 

191 

203 

360 

406 

100 

85 

16,500,000 

1.22 

20,100,000 

224 

236 

251 

448 

502 

200 

88 

28,400,000 

1.20 

34,000,000 

378 

400 

425 

756 

850 

300 

90 

39,000,000 

1.18 

46,000,000 

512 

542 

575 

1,024 

1,150 

400 

92 

47,800,000        1.18 

56,500,000 

628 

665 

707 

1,256 

1,415 

600 

95 

62,000,000 

1.17 

72,500,000 

806 

855 

905 

1,612 

1,810 

800 

95        74,200,000 

1.17 

87,000,000 

967 

1,025 

1,085 

1,935 

2,170 

1,000 

95 

84,200.000 

1.16 

97,700,000 

1,085 

1,150 

1,240 

2,170 

2,480 

1,500 

100 

97,500,000 

1.16 

113,000,000 

1,255 

1,330 

1.410 

2,510 

2,820 

2,000 

100 

110,000,000 

1.15 

126,500,000 

1,400 

1,490 

1,580 

2,800 

3,160 

3i6 


D  YNA  MO-ELE C TRIC  MA  CHINES. 


[§83 


TABLE  LXXIX. — SECTIONAL  AREA  OF  FIELD  MAGNET  FRAME  FOR  LOW- 
SPEED  RING  DYNAMOS. 


>, 

AREA  OP  FIELD  MAGNET  FRAME. 

»*b] 

•3    «  >M  8 

lal§ls 

3  3i« 

Average 
Useful 
Flux. 
(Table 
LX1V.) 
Lines  of 

Av'age 
Leak'ge 
Coeffi- 
cient. 
Table 
LXVIH 

Average 
Total 
Flux. 
*'. 
Lines  of 
force. 

Wr'ght 
Iron, 
Sm 

Cast 
Steel, 
Sm 

Mitis 
Iron, 
Sm 

Cast 
Iron, 
6.5*  AJ. 
Sm 

Cast 
Iron, 
ordin'y 
Sin 

I 

force. 

90,000 

85,000 

80,000 

45,000 

40,000 

D 

sq.  in. 

sq.  in. 

sq.  in. 

sq.  in., 

sq.  in. 

2.5 

25 

2,600,000 

1.50 

3,900,000 

43.3 

46 

48.7 

86.6 

97.5 

5 

26 

4,420,000 

1.45 

6,400,000 

71.2 

75.3 

80 

142.4 

160 

10 

28 

7.150.000 

1.40 

10,000,000 

111 

117.5 

125 

S22 

S50 

25 

30     1    14^200.000 

1.35 

19,200,000 

213.5 

226 

240 

417 

480 

50 

32 

24,200.000 

1.30 

31,500,000 

350 

.360 

394 

700 

788 

75 

33 

33,500,000 

1.25 

42,000,000 

467 

495 

525 

934 

1,050 

100 

35 

40,000,000 

1.22 

48,800,000 

543 

575 

610 

1,086 

1.220 

200 

40 

62,500,000 

1.20 

75,000,000 

833 

883 

938 

1,666 

1,875 

300 

42 

83.300,000 

1.18 

9S,500,000 

1,095 

1,160 

1,230 

2,190 

2,460 

400 

44 

100,000,000 

1.18 

118,000,000 

1,310 

1,390 

1,475 

2,620 

2,950 

600 

45 

131.000,000 

1.17 

153.500,000 

1,725 

.1,810 

1.940 

3,450 

3,880 

800 

45 

157,000,000 

1.17 

184,000,000 

2,050 

2,165 

2,300 

4,100 

4,600 

1,000 

45 

178,000.000 

1.16 

206,500,000 

2,300 

2,430 

2,580 

4,600 

5,160 

1,500 

45 

217,000.000 

1.16 

252.000,000 

2,800 

2,970 

3,150 

5,600 

6.300 

2,000 

45 

245,000,000 

1.15 

282,000,000 

3,140 

3,320 

3,525 

6,280 

7,050 

For  cases  of  practical  design,  in  which  the  fundamental  con- 
ditions materially  differ  from  those  forming  the  base  for  the 
above  tables,  the  areas  obtained  by  formula  (216)  may  also 
widely  vary  from  the  figures  given,  but,  by  proper  considera- 
tion, these  tables  will  answer  even  for  such  a  case,  and  will  be 
found  useful  for  comparing  the  results  of  calculations. 

83.  Dimensioning  of  Magnet  Cores. 

The  sectional  area  of  the  magnet  cores  being  found  by  means 
of  the  formulae  and  tables  given  in  §  82,  their  length  and  their 
relative  position  must  be  determined. 

a.   Length  of  Magnet  Cores. 

In  the  majority  of  types  the  length  of  the  magnet  cores  has 
a  more  or  less  fixed  relation  to  the  dimensions  of  the  armature, 
and  definite  rules  can  only  be  laid  down  for  such  cases  where 
the  length  of  the  magnets  is  not  already  limited  by  the  selec- 
tion of  the  type. 

Two  points  have  to  be  considered  in  dimensioning  the  length 
of  the  magnets.  The  longer  the  cores  are  made,  the  less 
height  will  be  taken  up  by  the  magnet  winding;  the  mean 
length  of  a  convolution  of  the  magnet  wire,  and,  consequently, 
the  total  length  of  wire  required  for  a  certain  magnetomotive 
force  will,  therefore,  be  smaller  the  greater  the  length  of  the 


§83] 


CALCULATION  OF  FIELD   MAGNET  FRAME. 


3*7 


core.  On  the  other  hand,  the  shorter  the  cores  are  chosen 
the  shorter  will  be  the  magnetic  circuit  of  the  machine,  ajidx  in 
consequence,  the  less  magnetomotive  force  will  be  required  to 
.set  up  the  necessary  magnetic  flux. 

Of  these  two  considerations— economy  of  copper  at  the  ex- 
pense of  additional  iron  on  the  one  hand,  and  saving  in  mag- 
netomotive force  and  in  weight  of  iron  on  the  other — the  latter 
predominates  over  the  former,  from  which  fact  follows  the 
.general  rule  to  make  the  cores  as  short  as  is  possible  without 
increasing  the  height  of  the  winding  space  to  an  undue  amount. 

In  order  to  enable  the  proper  carrying  out  of  this  rule,  the 
author  has  compiled  the  following  Table  LXXX.,  which  gives 
practical  values  of  the  height  of  the  winding  space  for  magnets 
of  various  types,  shapes  and  sizes: 

TABLE  LXXX.— HEIGHT  OF  WINDING  SPACE  FOR  DYNAMO  MAGNETS. 


BIPOLAR  TYPES. 

MULTIPOLAR  TYPES. 

SIZE  OF  CORE. 

Cylindrical 
Cores. 

Rectangular 
or 
Oval  Cores. 

Cylindrical 
Cores. 

Rectangular 
or 
Oval  Cores. 

..£ 

1 

M 

Diameter 
of 
Circular 
Cross-Section. 

Area 
of 
Rectangular 
or  Oval  Section. 

Height 
Winding  Space. 

Ratio  of 
Winding  Heighl 
to  Diameter  of  Coi 

Height 
of 
Winding  Space. 

>tio  of  Winding  H 
to  Diam.  of  Equa 
Circular  Section 

«     P. 

J3      02 
fl      ~ 
fe 

5  0 

§2 

Height 
of 
Winding  Space. 

atio  of  Winding  11 
to  Diam.  of  Eqiu 
Circular  Section 

3 

PH 

Ins. 

cm. 

Sq.  ins. 

Sq.  cm. 

Inch. 

Inch. 

Inch. 

Inch. 

j 

2.5 

.8 

4.9 

•t/ 

.50 

Q/ 

.75 

2 

5.1 

3.1 

20.4 

H 

.375 

"i" 

.50" 

1J4 

.625 

ji/ 

.75 

3 

7.6 

7.1 

45.4 

1 

.33 

iH 

.42 

19! 

.58 

2 

.67 

4 

10.2 

12.6 

81.7 

1/4 

.31 

18 

.38 

2 

.50 

2V<a 

.625 

6 

15.3 

28.3 

184 

ji2 

.25 

2 

.33 

.375 

2§i 

.46 

8 

20.3 

50.3 

324 

1M 

.22 

2^ 

.31 

2L| 

.31 

3 

.375 

10 

25.5 

78.5 

511 

jr? 

.19 

2-M 

.275 

2M 

.28 

3/4 

.33 

12 

30.5 

113.1 

731 

2 

.17 

3 

.25 

3 

.25 

3^9 

.29 

15 

38.1 

176.7 

1140 

.14 

314 

.22 

.22 

3% 

.25 

18 

45.7 

254.5 

1640 

2^4 

.125 

3V*> 

.20 

mz 

.20 

4 

.22 

21 

53.3 

346 

2231 

2% 

.113 

3-M 

.18 

3%. 

.18 

.215 

24 

61. 

452 

2922 

2J4 

.104 

4 

.17 

4 

.17 

5 

.21 

27 

68.6 

573 

3696 

2% 

.097 

4/4 

.16 

4/4 

.16 

5V<2 

.205 

30 

762 

707 

4560 

2'M 

.092 

4l/ 

.15 

41^ 

.15 

g 

.20 

33 

83.8 

855 

5515 

2% 

.087 

5 

.15 

4% 

.145 

Q\£ 

.197 

36 

91.5 

1018 

6576 

3 

.083 

5J-6 

.15 

5 

.14 

7 

.195 

3*8  DYNAMO-ELECTRIC  MACHINES.  [§  8S 

In  bipolar  machines,  such  as  the  various  horseshoe  types,  in 
which  the  length  of  the  magnet  cores  is  not  limited  by  the  form 
of  the  field  magnet  frame,  the  radial  height  of  the  magnet 
winding  in  case  of  cylindrical  magnets  varies  from  one-half  to 
one-twelfth  the  core  diameter,  according  to  the  size  of  the 
magnets,  and  in  case  of  rectangular  or  oval  magnets,  is  made 
from  .5  to  .15  of  the  diameter  of  the  equivalent  circular  cross- 
section.  For  multipolar  types,  in  which  the  length  of  the  mag- 
nets is  of  a  comparatively  much  greater  influence  upon  size 
and  weight  of  the  machine,  it  is  customary  to  set  the  limit  of 
the  winding  height  considerably  higher,  in  order  to  reduce  the 
length  necessary  for  the  magnet  winding.  For  cylindrical  mag- 
nets to  be  used  in  multipolar  machines,  therefore,  the  prac- 
tical limit  of  winding  height  ranges  from  .75  to  .14  of  the  core 
diameter,  and  for  rectangular  or  oval  magnets,  from  .75  to  .  195 
of  the  diameter  of  the  equivalent  circular  area,  according  to 
the  size. 

In  case  of  emergency  the  figures  given  for  rectangular  cores 
may  be  used  in  calculating  circular  magnets,  or  those  given  for 
multipolar  types  may  be  employed  for  bipolar  machines. 

In  order  to  keep  the  winding  heights  within  the  limits  given  in 
Table  LXXX.  the  lengths  of  cylindrical  magnets  have  to  be  made 
from  3  to  i  times  the  core  diameter  for  bipolar  types,  and  from 
i  to  \  the  core  diameter  for  multipolar  types;  those  of  rec- 
tangular magnets  from  i|  to  J  the  equivalent  diameter  for 
bipolar  types,  and  from  \\  to  f  the  equivalent  diameter  for 
multipolar  types;  and  the  lengths  of  oval  magnets,  finally, 
from  i£  to  |  the  diameter  of  the  equivalent  circular  area 
for  bipolar  types,  and  from  i|  to  f  the  equivalent  diameter 
for  multipolar  types. 

In  the  following  Tables  LXXXL,  LXXXIL,  LXXXIIL, 
and  LXXXIV.,  the  dimensions  of  cylindrical  magnet  cores  for 
bipolar  types,  of  cylindrical  magnet  cores  for  multipolar  types, 
of  rectangular  magnet  cores,  and  of  oval  magnet  cores,  respec- 
tively, have  been  calculated.  In  the  former  two  of  these 
tables  the  lengths  and  corresponding  ratios  are  given  for  cast- 
iron  as  well  as  for  wrought-iron  and  cast-steel  cores ;  in  the  latter 
two  for  wrought  /;wzand  cast  steel  only.  From  Tables  LXXXL 
and  LXXXIL  it  follows  that  cast-iron  cores  are  made  from  20 
to  10  per  cent,  longer,  according  to  the  size,  than  wrought-iron 


§83] 


CALCULATION  OF  FIELD   MAGNET  FRAME. 


319 


or  cast-steel  ones  of  the  same  diameter,  the  lengths  of  cast-iron 
cores  of  rectangular  or  oval  cross-section  can  therefore  be 
easily  deduced  from  the  figures  given  in  Tables  LXXXIII. 
and  LXXXIV. 


TABLE    LXXXI. — DIMENSIONS   OF    CYLINDRICAL    MAGNET   COKES  FOR 
BIPOLAR  TYPES. 


DIMENSIONS  OP  MAGNET  CORES,  IN  INCHES. 

TOTAL 

FLUX, 

Wrought  Iron  and  Cast  Steel. 

Cast  Iron. 

IN 

WEBEES. 

Diam. 

Length. 

Ratio 

Diam. 

Length. 

Ratio 

4n 

/» 

/m:4n 

<n 

/m 

/m:4n 

70,000 

1 

3 

3.0 

1* 

4* 

3.0 

150,000 

1* 

•3* 

2.5 

3* 

5* 

2.56 

275,000 

2 

4* 

2.25 

3 

7 

2.33 

425,000 

•3* 

5 

2.0 

3f 

8* 

2.20 

600,000 

3 

5£ 

1.92 

4* 

»* 

2.11 

850,000 

3i 

6 

1.86 

«i 

lOf 

2.05 

1,100,000 

4 

7i 

1.87 

6 

12 

2.0 

1,700,000 

5 

9 

1.80 

7i 

14* 

.9 

2,500,000 

6 

10| 

1.75 

9 

16* 

.83 

3,300,000 

7 

12 

1.72 

10* 

18 

.71 

4,500,000 

8 

13| 

1.70 

12 

20 

.67 

5,500,000 

9 

15 

1.67 

18* 

22 

.63 

7,000,000 

10 

16 

1,60 

15 

24 

.60 

8,500,000 

11 

17 

1.55 

16* 

85* 

.55 

10,000,000 

12 

18 

1.50 

18 

27 

.50 

15,000,000 

15 

22 

1.46 

22^ 

32 

.42 

22,500,000 

18 

25 

1.39 

27 

37 

1.37 

30,000,000 

21 

28 

1.33 

81* 

41 

1.30 

40,000,000 

24 

31 

.  1.29 

36 

45 

1.25 

50,000,000 

27 

34 

1.26 

.... 

.... 

60,000,000 

30 

36 

1.20 

.... 

.... 

.... 

75,000,000 

33 

38 

1.15 

.... 

.... 

.... 

90,000,000 

36 

40 

1.11 

.... 

.... 

.... 

b.   Relative  Position  of  Magnet  Cores. 

The  majority  of  types  having  two  or  more  magnets,  the  rela- 
tive position  of  the  magnet  cores  is  next  to  be  considered.  In 
a  great  number  of  forms,  having  the  magnets  arranged  symmet- 
rically with  reference  to  the  armature  circumference,  the  exact 
relative  position  of  the  magnet  cores  is  given  by  the  shape  of 
the  field  magnet  frame;  in  other  types,  however,  having  parallel 


320 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§83 


magnets  on  the  same  side  of  the  armature,  diametrically  or 
axially,  the  shape  of  the  frame  does  not  fix  their  relative 
position,  and  the  distance  between  them  is  to  be  properly 
determined. 

This  is  done  by  limiting  the  magnetic  leakage  across  the 
cores  to  a  certain  amount,  according  to  the  size  of  the  machine, 
namely,  from  about  33  per  cent,  of  the  useful  flux  in  small 
machines,  to  8  per  cent,  in  large  dynamos. 

The  relative  amount  of  the  leakage  across  the  magnet  cores 
is  determined  by  the  ratio  of  the  permeance  between  the 
cores  to  the  permeance  of  the  useful  path,  and  the  percentage 
of  the  core  leakage  is  kept  within  the  limits  given  above,  if  the 
average  permeance  of  the  space  between  the  magnet  cores 
does  not  exceed  one-third  of  the  permeance  of  the  gap-space 
in  small  machines,  and  one-twelfth  of  the  gap  permeance  in 
large  dynamos,  or  if  the  reluctance  across  the  core  is  at  least 
three  to  twelve  times,  respectively,  that  of  the  gaps. 


TABLE  LXXXIL—  DIMENSIONS  OP   CYLINDRICAL   MAGNET   CORES   FOR 
MULTIPOLAR  TYPES. 


DIMENSIONS  or  MAGNET  CORES,  IN  INCHES. 

TOTAL  FLUX 

PER 

Wrought  Iron  and  Cast  Steel. 

Cast  Iron. 

MAGNETIC 

CIRCUIT, 
IN  WBBEBS. 

Diam. 
4n 

Length. 

*m 

Ratio. 

£:.< 

Diam. 
4n 

Length, 
/m 

Ratio. 
/m  :  dm 

275,000 

2 

2 

1.00 

3 

a* 

1.17 

•       600,000 

3 

2f 

.92 

4* 

4* 

1.00 

1,100,000 

4 

3i 

.875 

6 

5i 

.92 

1,700,000 

5 

4 

.80 

n 

6f 

.90 

2,500,000 

6 

4* 

.75 

9 

8 

.89 

4,500,000 

8 

6 

.75 

12 

10| 

.875 

7,000,000 

10 

7i 

.75 

15 

13 

.87 

10,000,000 

12 

9 

.75 

18 

15 

.83 

15,000,000 

15 

11 

.73 

22i 

18 

.80 

22,500,000 

18 

13 

.72 

27 

20 

.74 

30,000,000 

21 

144- 

.69 

81| 

22 

.70 

40,000,000 

24 

16" 

.67 

36 

24 

.67 

50,000,000 

27 

17 

.63 

.... 

... 

60,000,000 

30 

18 

.60 

.... 

.... 

.... 

75,000,000 

33 

19 

.58 

.... 

.... 

.... 

90,000,000 

36 

20 

.56 





§83]         CALCULATION  OF  FIELD   MAGNET  FRAME.  321 


TABLE    LXXXIII. — DIMENSIONS    OP    RECTANGULAR    MAGNET    CORES. 
(WROUGHT  IRON  AND  CAST  STEEL.) 


TOTAL  FLUX 

PER 

MAGNETIC 
CIRCUIT, 
IN  WBBERS. 

CROSS-SECTION. 

LENGTH. 

Breadth, 
Inches. 

fl 

T3     0 
gl 

Area, 
Square  Inches. 

Diam. 
of 

Equiv. 
Circular 
Area 

«n 

Bipolar  Types. 

Multipolar  Types. 

Length 
^m 

Ratio 

C:4n 

Length 
'm 

Ratio 

/»:*» 

500,000 
700,000 
1,000,000 
1,400,000 

2 
2 
2 
2 

3 

4 
6 
8 

6 
8 
12 
16 

sfl 

4^ 

9* 
5* 

1.64 
1.57 
1.40 
1.33 

S* 

¥ 

1.27 
1.25 
1.14 
1.11 

1,200,000 
1,600,000 
2,400,000 
3,200,000 

2,000,000 
2,750,000 
4,250,000 
5,500,000 

3 
3 
3 
3 

t1 

9 

12 

6 

8 
12 
16 

13.5 

18 
27 
36 

24 
32 

48 
64 

4il 
5% 

9 

i 

1.31 
1.30 
1.28 
1.26 

1~26 
1.26 
1.24 
1.20 

P 

6 
6^ 

1.08 
1.04 
1.02 
.96 

4 
4 
4 
4 

8 
9% 
10% 

5M 
6^^ 

1.03 
.98 
.95 
95 

4,750,000 
6,500,000 
9,500,000 
12,500,000 

6 
6 
6 
6 

9 
12 
18 
24 

54 
72 

108 
144 

1 

10 

111^ 

1.20 
1.20 
1.15 
1.15 

8 
9 
11 
12^ 

.96 
.94 
.94 
.93 

8,500,000 
11,000,000 
17,000,000 

8 
8 
8 

12 
16 
24 

96 
128 
192 

11 

13 
15 
lift 

1.18 
1.18 
1.12 

8* 

14 

.96 
.94 
.90 

13,000,000 
17,500,000 
26,000,000 

10 
10 
10 

15 
20 
30 

150 
200 
300 

13% 
16 
19^ 

16 
18 
20 

1.15 
1.12 
1.03 

g* 

16 

.90 
.875 
.82 

.90 
.84 

.77 

19,000,000 
25,000,000 
38,000,000 

12 
12 
12 

18 
24 
36 

216 
288 
432 

18 
20 
22 

1.08 
1.05 
.94 

15 
16 
18 

30,000,000 
40,000,000 
50,000,000 

15 

15 
15 

to2* 

•3% 

337.5 
450 
562.5 

s* 

26% 

20 
22 
24 

.96 
.92 
.90 

17 
18 
19 

.82 
.75 
.71 

38.000,000 
47,500,000 
57,000,000 

18 
18 
18 

24 
30 
36 

432 

540 
648 

630 
756 

882 

~28%~ 
31 
33^ 

22 

24 
25 

.94 
.915 
.87 

18 
19 
20 

.765 
.74 
.70 

.71 
.68 
.66 

55,000,000 
66,000,000 
77,000,000 

21 
21 
21 

30 
36 
42 

25 
26 
27 

.85 
.83 
.81 

20 
21 
22 

75.000,000 
90,000,000 
100,000,000 

24 
24 
24 

36 
42 

48 

864 
1008 
1152 

i 

27 

28 
30 

.81 
.80 
.785 

22 
23 
24 

.66 
.66 
.64 

The  area  of  the  cross-section  and  the  length  of  the  cores 
being  given,  the  reluctance  of  the  space  between  them  depends 
upon  the  shape  of  their  cross-section  and  upon  the  distance 
between  them.  In  case  of  round  cores  the  shape  is  given  by 


322 


DYNAMO-ELECTRIC  MACHINES. 


TABLE   LXXXIV. 


DIMENSIONS  OF  OVAL  MAGNET  COKES. 
IRON  AND  CAST  STEEL.) 


(WROUGHT 


TOTAL  FLUX 

PER 

MAGNETIC 
CIRCUIT, 
IN  WBBERS. 

CROSS-SECTION. 

LENGTH. 

Breadth, 
»°wl®  1  Inches. 

~£ 

a| 
pj 

4 
6 

8 

I 

ft 

jf 

Diameter 
of 
Equiv. 
Circular 
Area 

4 

Bipolar  Types. 

Multipolar  Types. 

Length 

/m 

Inches. 

Ratio 

/m:<4 

Length 

An 
Inches. 

Ratio 
/»:4n 

600,000 
1,000,000 
1,300,000 

7.14 
11.14 
15.14 

3 

64 

1.50 
1.40 
1.37 

5  4 

1.17 
1.18 

1.14 

1,400,000 
2,200,000 
3,000,000 

3 
3 
3 

4 
4 
4 

6 
9 
12 

16.06 
25.06 
34.06 

i 

6 

1.33 
1.33 

1.28 

5 
6 

7 

6 

1.11 
1.07 
1.05 

2,500,000 
3,900,000 
5,250,000 

8 
12 
16 

28.56 
44.56 
60.56 

6 

11  4 

1.29 
1.27 
1.26 

1.00 
1.00 
.97 

5,500,000 
8,750,000 
12,000,000 

6 
6 
6 

12 
18 
24 

64.26 
100.26 
136.26 

9 

tiu 

13j| 

11 
13 
15 

1.22 
1.16 
1.14 

12 

.945 
.93 
.915 

10,000,000 
15,000,000 

8 
8 

10 
10 

16 
24 

114.14 
178.14 

12 
15 

14 
16 

1.17 
1.065 

1.065 
1.065 

11 
13 

.92 

.87 

15,000,000 
24,000,000 

20 
30 

178.5 
278.5 

15 

18% 

16 
20 

13 
16 

.87 
.85 

22,500,000 
35,000,000 

12 
12 

24 

36 

257 
401 

18 
M*fi 

28J4 

18 
21 

1.00 
.93 

15 
17 

.835 
.755 

35,000,000 
55,000,000 

15 
15 

30 
45 

400 
625 

21 
25 

.93 

.885 

17 
20 

.755 
.71 

50,000,000 
P0,000,000 

18 
18 

36 
42 

578 
686 

IS 

24 
25 

.885 
.85 

19 
20 

.70 
.68 

70,000,000 
80,000,000 

21 
21 

42      i  787 
48      i  913 

31% 
34^g 

26 
27 

.82 
.79 

21 
22 

.66 
.645 

90,000,000 
100,000,000 

24 
24 

48 
54 

1028 
1172 

§t 

28 
30 

.    .78 
.78 

& 

.625 
.62 

the  area  of  the  cross-section,  and  the  reluctance  of  the  path 
from  core  to  core,  in  consequence,  only  depends  upon  their 
distance  apart,  directly  increasing  with  the  same.  The  reluc- 
tance of  the  air  gaps  is  determined  by  the  diameter  and  length 
of  the  armature,  by  the  percentage  of  polar  embrace,  and  by 
the  radial  length  of  the  gap-space,  decreasing  with  the  area 
of  the  gap  and  increasing  with  its  length.  The  cross-section  of 
the  cores  and  the  gap  area,  both  depending  upon  the  output 
of  the  machine,  have  a  more  or  less  fixed  relation  to  each 
other — varying  with  the  type,  the  voltage,  the  speed,  and  the 


§83] 


CALCULATION  OF  FIELD  MAGNET  FRAME. 


323 


kind  of  armature — and  the  relation  between  the  reluctance 
across  the  cores  to  that  of  the  air  gaps  can  approximately  be 
expressed  by  the  ratio  of  the  average  distance  apart  of  the 
cores  to  the  radial  length  of  the  gap-space.  In  dynamos  with 
smooth-drum  armature  this  ratio  is  made  from  6  to  16,  in  smooth- 
ring  machines  from  8  to  20,  and  for  toothed  and  perforated 
armatures  the  distance  apart  of  the  cores  is  taken  from  3  to  6 
times  the  maximum  radial  length  of  the  gap-space,  /.  <?.,  from 
3  to  6  times  the  distance  between  pole  face  and  bottom  of 
armature  slot.  The  following  Table  LXXXV.  gives  the 
average  distance  between  cylindrical  magnet  cores  for  various 
kinds  and  sizes  of  armatures,  the  ratio  of  this  distance  to  the 
radial  length  of  the  gap-space,  and  the  corresponding  approxi- 
mate leakage  between  the  magnet  cores,  expressed  in  per  cent, 
of  the  useful  flux: 

TABLE  LXXXV. — DISTANCE  BETWEEN   CYLINDRICAL   MAGNET   CORES. 


SMOOTH  CORE  ARMATURE. 

TOOTHED  OR 

of 

PERFORATED  ARMATURE. 

1 

Drum. 

Ring. 

Diameter  of  Arm 
Inches. 

Radial  Length 
of 
Gap  Space. 

Least  Distance 
between  Cores. 

Ratio 
of  Distance  Apart 
to  Length  of  Gap. 

Approx.  Leakage 
between  Cores 
p.  c.  of  Useful  Flux. 

Radial  Length 
of  Gap  Space. 

Least  Distance 
between  Cores. 

Ratio 
of  Distance  Apart 
to  Length  of  Gap. 

Approx.  Leakage 
between  Cores 
p.  c.  of  Useful  Flux. 

Max.  Radial  Length 
of  Gap  Space. 

Least  Distance 
between  Cores. 

Ratio 
of  Distance  Apart 
Max.  Length  of  Gap. 

Approx.  Leakage 
between  Cores 
p.  c.  of  Useful  Flux. 

c 

J3 

a 

.2 

2 

ii> 

2    " 

'  5.8 

33£ 

3    ' 

H 

2% 

6  3 

30 

4 

3 

6.9 

25 

T5s" 

94" 

8.0 

20% 

ii* 

2    " 

2.9 

15* 

6 

8 

7.5 

22 

11 

3 

8.7 

18 

13 

2Vfs 

3.1 

14 

8 

T91T 

4J4 

8.0       20 

% 

<$4 

10.0 

16 

it 

3J4 

3.5 

13 

10 

R 

5V« 

8.8 

18 

13 

flZ 

11.7 

14 

JL 

4 

3.8 

12 

12 

it 

7 

10.2 

16 

7 

5% 

13.1 

12 

3 

4.0 

11 

15 

II 

8^ 

11.3 

14 

i; 

7 

14.9 

11 

2 

5^Z 

4.2 

10 

18     i    M 

10 

12.3 

12 

t^ 

8/4 

16.5 

10 

\/ 

gi2 

4.3 

10 

21      i     $ 

12 

13.5 

10 

T95 

9^ 

16.9 

9^ 

% 

7iJ 

4.6 

9^ 

25      i    « 

14 

15 

9 

R£ 

11 

17.6 

9 

&A 

8Va 

4.9 

9 

30        i" 

16 

16 

S 

11 

13 

18.9 

$4 

1^| 

10 

5.3 

8^ 

40    !'  Ifc 

18 

16 

8 

M 

15 

20 

8 

2 

12 

6 

8 

In  case  of  inclined  cylindrical  magnets  the  figures  given  in 
Table  LXXXV.  for  the  least  distances  apart  are  to  be  consid- 
ered as  the  mean  least  distances,  taken  across  the  magnets 
midway  between  their  ends.  (Compare  formula  180,  §  65.) 


324 


DYNAMO-ELECTRIC  MACHINES. 


[§83 


In  dynamos  with  rectangular  and  oval  cores  the  leakage 
across,  for  the  same  distance  apart,  is  greater  than  in  case  of 
circular  cores  of  equal  sectional  area,  increasing  in  proportion 
to  the  ratio  of  the  width  of  the  cores  to  their  breadth.  For 
rectangular  and  oval  cores,  therefore,  the  distance  apart  is  to 
be  made  greater  than  for  round  cores  in  order  to  limit  the 
leakage  between  them  to  the  same  amount;  and  the  distance 
must  be  the  greater  the  wider  the  cores  are  in  proportion  to 
their  thickness.  The  following  Table  LXXXVI.  gives  the 
minimum,  average  and  maximum  values  of  the  ratio  of  the  dis- 
tance across  rectangular  and  oval  cores  of  various  shapes  of 
cross- sections  to  the  distance  which,  between  round  cores  of 
equal  sectional  area,  effects  approximately  the  same  leakage, 
in  small,  in  medium-sized,  and  in  large  dynamos,  respectively: 

TABLE    LXXXVI. — DISTANCE    BETWEEN    RECTANGULAR     AND     OVAL 
MAGNET  CORES. 


RATIO 

OP 

THICKNESS 

Distance  between  Rectangular  and   Oval   Magnet   Cores,  as 
compared  with  that  between  Round  Cores  of  Equal  Area, 
causing  approximately  the  same  leakage  across. 

TO  \VlDTH 

OF 

CORES. 

Minimum. 
(Small  Machines.) 

Average. 

Maximum. 
(Large  Machines.) 

1          1 

1.0 

1.0 

.0 

3          4 

1.05 

1.07 

.1 

2          3 

1.1 

1.15 

.2 

1          2 

.15 

.22 

.3 

1          3 

.2 

.3 

.4 

4 

.25 

.37 

.5 

5 

.3 

.45 

.6 

6 

.35 

.55 

.75 

7 

1.4 

.65 

.9 

8 

1.5 

.75 

2.05 

1         9 

1.6 

.9 

2.25 

1        10 

1.7 

2.1 

2.5 

In  order  to  determine  the  proper  distance  apart  of  rectan- 
gular and  oval  magnet  cores,  the  corresponding  distance  be- 
tween round  cores  of  equal  cross-section  is  taken  from  Table 
LXXXIIL,  in  multiplying  the  radial  length  of  the  gap-space 
by  the  ratio  of  distance  apart  to  length  of  gap  for  the  particu- 
lar size  of  armature.  The  distance  thus  obtained  is  then  mul- 
tiplied by  the  respective  figure  found  for  the  shape  in  question 
from  Table  LXXXVI. 


§85]         CALCULATION  OF  FIELD  MAGNET  FRAME.          325 

84.  Dimensioning  of  Yokes. 

In  bipolar  types — the  dimensions  of  the  magnet  cores  being 
given  by  Tables  LXXXL,  LXXXIII.  or  LXXXIV.,  §  83,  and 
their  least  distance  apart  by  Table  LXXX.  or  LXXXVL,  §  83, 
thus  fixing  the  length  of  the  yoke,  and  the  sectional  area  of 
the  yokes  being  found  from  formula  (216),  §  82 — the  dimen- 
sioning of  the  yoke  consists  in  arranging  its  cross-section  with 
reference  to  the  shape  of  the  section  of  the  cores,  and,  for  the 
case  that  its  material  is  different  from  that  of  the  cores,  in 
providing  a  sufficient  contact  area,  conforming  to  the  rules 
given  in  §  80. 

In  multipolar  types  the  total  cross-section  found  for  the 
frame  from  formula  (216),  §  82,  is  to  be  divided  by  the  total 
number  of  magnetic  circuits  in  the  machine  and  multiplied  by 
the  number  of  circuits  passing  through  any  part  of  the  yoke 
in  order  to  obtain  the  sectional  area  required  for  that  part  of 
the  yoke;  otherwise  the  above  rules  also  govern  the  dimen- 
sioning of  the  yokes  for  multipolar  machines. 

85.  Dimensioning  of  Polepieces. 

In  dimensioning  the  polepieces,  three  cases  have  to  be  con- 
sidered: (i)  the  path  of  the  lines  of  force  leaving  the  pole- 
pieces  has  the  same  direction  as  their  path  through  the 
magnets  (Fig.  251);  (2)  the  path  of  the  lines  leaving  the  pole- 


FlQ.251     FlQ.252         FIG.  253         FlQ.  254 


Figs.  251  to  255. — Various  Kinds  of  Polepieces. 

pieces  makes  a  right  angle  to  that  through  the  cores  (Fig.  252); 
and  (3)  the  path  of  the  lines  leaving  the  polepieces  is  parallel 
but  of  opposite  direction  to  that  through  the  cores,  making 
two  turns  at  right  angles  in  the  polepieces  (Fig.  253). 

In  the  first  case,  Fig.  251,  which  occurs  in  dynamos  of  the 
iron-clad,   the  radial  and  the  axial  multipolar  types,  the  shape 


326 


DYNAMO-ELECTRIC  MACHINES. 


[$85 


of  the  cross-section  is  fixed  by  the  form  of  the  magnet  core  at 
one  end  and  by  the  axial  length  or  the  radial  width  of  the 
armature,  respectively,  and  the  percentage  of  polar  arc  at  the 
other,  while  the  height ,  in  the  direction  of  the  lines  of  force,  is 
to  be  made  as  small  as  possible,  in  order  not  to  increase  the 
total  length  of  the  magnetic  circuit  more  than  necessary. 

TABLE  LXXXVII. — DIMENSIONS  OF  POLEPIECES  FOR  BIPOLAR  HORSE- 
SHOE TYPE  DYNAMOS. 


DRUM  ARMATURE. 

RING  ARMATURE. 

I 

3 

Dimensions  of 
Polepiece. 

£ 

Dimensions  of  Polepiece. 

o 

S        0 

'3 

Thick-      5     § 

1 

I 

p 

5 

•  15 

ness  in 

S    •£ 

. 

Area    in  Centre 

M 

§     !lL 

IH 

1    |? 

Centre. 

•^           OB    O-aJ 

•<«' 

1 

Square  Inches. 

2 

1     o£l 

•—  J2 

2    iJ  * 

Inches. 

•^      o  ^*  ^* 

.*.£ 

V 

N 

HoW^| 

O  W 

*     Hi 

^— 

— 

&»^w^| 

O  0 
u  C 

5 

1 

a  31* 

i  a^ 

5 

JO 

Jf 

53 

tD 

=  co 

fl 

|| 

1  ll^ 

QJ  HH 

1 

« 

sp 

Wrought 
Iron. 

Cast 
Iron. 

a 

•<  w 

5 

O 

3 

&* 

5  e 

- 

PQ 

.1 

350.000 

If 

2| 

34 

49 

1 

175,000 

4 

4f 

| 

If 

.25 

500,000 

2i 

8 

a 

250,000 

5 

5f 

a 

24 

.5 

650,000!  2f 

^4 

6i 

t 

a 

325,000 

6 

6f 

1 

900,000!  3i 

4 

6 

1 

a 

450,000 

7 

7f 

8* 

44 

2 

l,400,000i  3f 

44 

7 

1 

2 

675,000 

8 

9 

3| 

6f 

3 

1,800,000 

44. 

5! 

8i 

a 

2i 

900,000 

94 

104 

44 

9 

5 

2,500,000 

^i 

6i 

94 

if 

1,300,000 

11 

12 

13 

10 

3,500,000 

6 

7 

104 

it 

3| 

2,100,000 

14 

15 

104 

21 

15 

5,000,000 

6| 

7f 

12 

at 

2,800,000 

15 

16 

14 

28 

20 

6,000,000 

74 

8| 

13 

4* 

3,500.000 

16 

17 

174 

35 

25 

7,000,000 

8|. 

9| 

14 

24 

5 

4,200,000 

18 

19 

21 

42 

30 

8,000,000 

9 

15 

2f 

5| 

4,800,000 

20 

21 

24 

48 

50 

12,500,000 

104 

HI 

18 

7 

7,000,000 

24 

25 

35 

70 

75 

16,500,000 

12-i 

131 

20 

44 

8i 

9,500,000 

28 

29J 

474 

95 

100 

21,000,000 

15 

22 

4f 

94 

12,000,000 

32 

334 

60 

120 

150 

30,000,000 

184 

20i 

26 

Sf 

114 

17,000,000 

36 

374 

85 

170 

200 

38.000,000 

31 

64 

21,500,000 

40 

42 

107* 

215 

300 

57iOOO,000 

28 

38 

74 

15 

30,000,000 

46 

48 

150^ 

300 

In  the  second  case,  Fig.  252,  met  with  in  bipolar  and  multi- 
ple horseshoe  and  in  tangential  multipolar  types,  the  height  of 
the  polepieces  is  determined  by  the  diameter,  and  the  length 
of  the  polepiece  by  the  length  of  the  armature,  while  the  area 
of  the  cross-section,  perpendicular  to  the  flow  of  the  lines,  is 
to  be  made  of  the  size  obtained  by  formula  (216)  at  the  end 
next  to  the  magnet  core,  and  to  be  gradually  decreased  in 
amount  from  that  end  to  the  opposite  end  or  to  the  centre  of 


§85]         CALCULATION  OF  FIELD  MAGNET  FRAME.  327 

the  polepiece,  respectively,  according  to  whether  there  is  but 
one  magnetic  circuit,  or  whether  two  circuits  are  parsing 
through  the  same  polepiece.  Since,  in  bipolar  machines,  the 
lines  of  force  are  supposed  to  divide  equally  between  the  two 
halves  of  the  armature,  only  one-half  of  the  total  flux  passes 
the  centre  of  the  polepieces,  in  order  to  reach  the  half  of  the 
armature  opposite  the  magnets,  and  the  area  in  the  centre  of 
the  polepiece  consequently  needs  to  be  but  one-half  that  at  the 
end  next  to  the  core.  In  case  the  two  circuits  passing  through 
each  polepiece,  Fig.  254,  the  same  applies  to  the  cross-section 
of  the  polepiece,  at  one-quarter  the  height  from  either  end. 
For  ready  use,  in  the  preceding  Table  LXXXVIL,  the  dimen- 
sions of  wrought-  and  cast-iron  polepieces  for  various  sizes  of 
bipolar  horseshoe  type  dynamos  are  calculated  for  drum  and 
ring  armatures,  by  combining  the  respective  data  given  in 
former  tables. 

In  the  third  case,  Fig.  253,  finally,  which  is  found  in  single 
and  double  magnet  types,  the  length  of  the  magnetic  circuit  in 
the  polepiece  is  determined  by  the  diameter  of  the  armature, 
by  the  cross-section  of  the  magnet  core,  and  by  the  height  of 
their  winding  space;  the  width,  parallel  to  the  armature  shaft 
of  the  polepiece  near  the  magnet,  is  given  by  the  width  of  the 
magnet  core,  and  that  near  the  armature  by  the  axial  length  of 
the  latter.  The  heights,  parallel  to  the  axis  of  the  magnet 
core,  in  case  of  a  single  circuit,  are  to  be  so  chosen  that  all  of 
the  cross-sections,  up  to  that  in  line  with  the  pole  corner  next 
to  the  magnet  core,  have  an  area  at  least  equal  in  amount  to 
that  obtained  by  formula  (216),  and  that  the  section  in  line 
with  the  armature  centre  has  an  area  of  one-half  that  amount. 
In  case  of  two  circuits  meeting  at  the  polepieces  (consequent 
pole  types).  Fig.  255,  the  full  area  has  to  be  provided  from 
either  end  of  the  polepiece  to  the  sections  in  line  with  the  pole 
corners,  half  the  full  area  at  quarter  distance  from  each  pole 
corner,  that  is,  midway  between  each  pole  corner  and  the 
pole  centre,  and  sufficient  cross-section  for  mechanical 
strength  only  is  needed  at  the  centre  of  the  polepiece. 


PART  V. 


CALCULATION  OF  MAGNETIZING  FORCES. 


CHAPTER  XVII. 

THEORY    OF    THE    MAGNETIC  CIRCUIT 

86.  Law  of  the  Magnetic  Circuit. 

The  magnetic  flux  through  the  various  parts  of  the  mag- 
netic circuit  being  known  by  means  of  formulae  (137),  §  56, 
and  (156),  §60,  respectively,  and  the  dimensions  of  the  magnet 
frame  being  determined  by  the  rules  and  formulae  given  in 
Chapters  XV.  and  XVI.,  the  magnetomotive  force  necessary  to 
drive  the  required  flux  through  the  circuit  of  given  reluctance 
can  now  be  calculated  by  virtue  of  the  "Law  of  the  Mag- 
netic Circuit." 

For  the  magnetic  circuit  a  law  holds  good  similar  to  Ohm's 
Law  of  the  electric  circuit;  in  the  electric  circuit: 

Electromotive   Force 
Current  (or  Electric  Flux)  = 


and  analogously,  in  the  magnetic  circuit: 

Magnetomotive  Force 
Magnetic  Flu*   ,  Reiuctance  --  ' 

from  which  follows: 

Magnetomotive  Force  —  Magnetic    Flux  x  Reluc- 

tance ...................  ....................  (222) 

The  Reluctance  of  a  magnetic  circuit,  similar  to  the  electric 
case  of  resistance,  can  be  expressed  by  the  specific  reluctance, 
or  reluctivity,  of  the  material,  and  the  dimensions  of  the  mag- 
netic conductor,  thus: 

Reluctance  =  Reluctivity  X   LengtlL  . 

Area 

But  the  reluctivity  of  a  magnetic  material  is  the  reciprocal 
of  its  permeability  (similarly  as  the  resistivity  of  an  electric  con- 
ducting material  is  the  reciprocal  of  its  conductivity),  and  con- 
sequently we  have: 

Reluctance  =  =  -  KL,ength  -      .....  (223) 
Permeability  X  Area 


332  DYNAMO-ELECTRIC  MACHINES.  [§87 

Combining  (222)  and  (223),  we  obtain: 

Magnetomotive    Force  =   Magnetic  Flux  X      LenSth 

Area  Permeability 

and  since  the  quotient  of  magnetic  flux  by  area  is  the    mag- 
netic density,  we  have : 

Magnetomotive   Force   =  Magnetic  Density   x     L         h 

Permeability 

The  permeability  of  magnetic  materials  depending  upon  the 
magnetic  density  employed  in  the  circuit,  see  Table  LXXV., 
§  81,  the  quotient  of  magnetic  density  and  permeability  also 
depends  upon  the  density,  and  has  a  fixed  value  for  every 
degree  of  saturation  and  for  each  material.  But  this  quotient 
multiplied  by  the  length  of  the  circuit  gives  the  magneto- 
motive force  required  for  that  circuit,  and  consequently 
represents  the  magnetomotive  force  per  unit  of  length,  or  the 
specific  magnetomotive  force  of  the  circuit.  In  order  to  obtain  the 
M.M.F.  required  for  any  material,  any  density  and  any  length, 
therefore,  the  specific  M.  M.  F.  for  the  respective  material  at 
the  density  employed  is  to  be  multiplied  by  the  length  of  the 
circuit: 

Magnetomotive  Force  =  Specific  M.  M.  F.  x  Length.     (224:) 

87.  Unit    Magnetomotive     Force. — Relation      Between 
Magnetomotive  Force  and  Exciting  Power. 

An  infinitely  long  solenoid  of  unit  cross-sectional  area  (i 
square  centimetre),  having  unit  magnetizing  force  or  exciting 
power  (i  current-turn)  per  unit  of  length  (i  centimetre)  pos- 
sesses poles  of  unit  strength  at  its  ultimate  extremities.  If  the 
exciting  power  per  centimetre  length,  therefore,  is  i  ampere- 
turn,  /.  e.,  y1^  of  a  current-turn  (the  ampere  being  the  tenth 
part  of  the  absolute  unit  of  current-strength),  the  poles  pro- 
duced at  the  ends  of  the  solenoid  will  be  of  the  strength  of  ^ 
of  a  unit  pole. 

Since  a  unit  pole  disperses  4  n  lines  of  force,  or  webers,  see 
§  55,  the  magnetic  flux  of  a  unit  solenoid  of  infinite  length  and 
of  a  specific  exciting  power  of  i  ampere-turn  per  centimetre  is 

4  it 

webers. 


§88]  THEORY  OF   THE  MAGNETIC  CIRCUIT.  333 

and  the  density  of  the  flux  is 

4  TT  4  it 

webers  per  square  centimetre  ',  or        —  gausses. 

The  reluctance  per  unit  length  of  the  solenoid,  the  latter 
being  of  i  square  centimetre  sectional  area,  is  that  of  i  cubic 
centimetre  of  air,  and  therefore  is  unity,  or  i  oersted,  hence 
the  M.  M.  F.  of  the  coil  per  ampere-turn  of  exciting  power 
being  the  product  of  magnetic  flux  and  reluctance,  is 

4_7T 

10 
C.  G.  S  units  of  magnetomotive  force,  or 

—  gilberts. 
A  magnetomotive  force  of 

—  gilberts 

being  excited  by  one  ampere-turn  of  magnetizing  force,  and 
the  magnetomotive  force  being  proportional  to  the  magnet- 
izing force  producing  the  same,  it  follows  that  the  entire 
M.  M.  F.  of  a  circuit,  in  gilberts,  is 

4J7T 

10 

times  the  total  number  of  ampere-turns;  and  inversely,  in 
order  to  express  the  exciting  power  necessary,  to  produce  a 
certain  M.  M.  F.,  the  number  of  gilberts  to  be  multiplied  by 


10 

-.796; 


thus: 


Number  of  Ampere-turns  =  —    x  Number  of   Gil- 

4  n 


berts 


88.  Magnetizing  Force  Required  for  any  Portion  of  a 
Magnetic  Circuit. 

The  magnetizing  force  required  for  any  circuit   is   the  sum 
of  the  magnetizing  forces  used  for  its  different  parts. 


334  DYNAMO-ELECTRIC  MACHINES.  [§88 

From  (224)  and  (225),  §87,  follows  that  the  exciting  power 
required  for  any  part  of  a  magnetic  circuit  is 

10 

4  n 

times  the  product  of  the  specific  M.  M.  F.  and  the  length  of 
that  portion  of  the  circuit: 

Magnetizing   Force  =  -1^-   x    Specific  M.  M.  F.   x    Length. 
4  n 

The   product  of  the   specific   magnetomotive   force,   for  the 
particular  material  and  density  in  question,  with  the  constant 

factor 

10 

*$?. 

represents  the  exciting  power  per  unit  length  of  the  circuit, 
or  the  Specific  Magnetizing  Force;  consequently  we  have: 

Magnetizing  Force  —  Specific  Magnetizing  Force  X  Length, 
or, 

Number  of  Ampere-turns 

=  Ampere-turns  per  unit  of  Length  x  Length. 

Denoting  the  density  of  the  lines  of  force  in  any  particular 
portion  of  a  magnetic  circuit  by  (B,  the  specific  magnetizing 
force,  being  a  function  of  the  same,  by  /  ((B),  and  the  length 
by  /,  the  number  of  ampere-turns  required  for  that  portion 
of  the  magnetic  circuit  can  be  calculated  from  the  general 
formula: 

at  =/    <B)  X  /,      (226) 

where/((B)  =  Specific  magnetizing  force,  in  ampere-turns  per 
inch,  or  per  centimetre,  of  length,  for  the 
particular  material  and  density  employed,  see 
Tables  LXXXVIII.  and  LXXXIX.,  or  Fig.  256; 
/=  length  of  the  magnetic  circuit  in  the  respec- 
tive material  in  inches,  or  centimetres,  re- 
spectively. 

The  values  of  the  specific  magnetizing  forces,  /  (&),  for 
various  densities,  as  averaged  from  a  great  number  of  tests  by 


§88]  THEORY  OF   THE  MAGNETIC  CIRCUIT.  335 

Ewing,1  Negbauer,2  Kennelly,3  Steinmetz,4  Thompson,6  and 
others,  for  the  various  materials  are  compiled  in  the  following 
Tables  LXXXVIII.  and  LXXXIX.,  which  give  the  specific 
magnetizing  force  in  ampere-turns  per  inch  length,  and  in 
ampere-turns  per  centimetre  length,  respectively. 

The  figures  in  the  last  column  of  these  tables,  referring  to 
air,  are  obtained  by  multiplying  the  magnetic  density,  (&,  by 

10 
4?r 
in  the  metric,  and  by 

10  I 


in  the  English  system;  for  in  case  of  air,  the  permeability, 
being  unity,  does  not  depend  upon  the  density,  and  the  mag- 
netizing force,  in  consequence,  is  a  direct  function  of  the  air 
density,  5C  (here  &). 

For  convenient  reference  the  values  of  /(<B)  contained  in 
Tables  LXXXVIII.  and  LXXXIX.,  for  the  various  kinds  of 
iron,  are  plotted  in  Fig.  256,  p.  338. 

The  said  Tables  LXXXVIII.  and  LXXXIX.,  although 
carefully  averaged  with  reference  to  commercial  tests  of 
various  kinds  of  iron,  cannot  be  expected  to  give  accurate 
results  in  specific  cases  of  actual  design,  since  different  sam- 
ples of  one  and  the  same  kind  of  iron  often  vary  as  much  as 
10  per  cent,  and  more  in  permeability.  These  tables  are, 
therefore,  intended  only  for  the  use  of  the  student,  while  the 
practical  designer  is  supposed  to  make  up  his  own  table  or 


1  J.  A.  Ewing,    "Magnetism  in  Iron  and  Other  Metals,"  The  Electrician 
(London,  1890-91). 

2  Walter  Negbauer,  Electrical  Engineer ',  vol.  ix.  p.  56  (February,  1890). 

3  A.  E.  Kerinelly,  Trans.  Am.  Inst.  El.  Eng.t  vol.  viii.  p.  485  (October  27, 
1891)  ;  Electrical  Engineer,   vol.   xii.  p.  508  (November  4,  1891);    Electrical 
World,  vol.  xviii.  p.  350  (November  7,  1891). 

4  Charles  P.  Steinmetz,  Trans.  Am.  Inst.  El.  Eng.,  vol.  ix.  p.  3  (January 
19,  1892);  Electrical  Engineer,  vol.  xiii.  pp.  91,  121,  143,  167,  261,  282  (Jan- 
uary 27,  February  3,  10,  17,  March  9,  16,  1892);  Electrical  World,  vol.  xix.  pp. 
73.  89  (January  30,  February  6,  1892). 

6  Milton  E.  Thompson,  Percy  H.  Knight,  and  George  W.  Bacon,  Trans. 
Am.  Inst.  El.  Eng.,  vol.  ix.  p.  250  (June  7,  1892);  Electrical  Engineer,  vol. 
xiv.  p.  40  (July  13,  1892);  Electrical  World,  vol.  xix.  p.  436  (June  25,  '892). 


336 


DYNAMO-ELECTRIC  MACHINES. 


[§88 


TABLE    LXXXVIIL— SPECIFIC    MAGNETIZING    FORCES    FOB    VARIOUS 
MATERIALS  AT  DIFFERENT  DENSITIES,  IN  ENGLISH  MEASURE. 


MAGNETIC     | 
DENSITY. 

UNIT  MAGNETIZING  FORCE. 
Ampere-Turns  per  Inch  Length. 

Lines  of  Force 

per  square 
inch. 

<a" 

Annealed 
Wrought 
Iron. 

Soft 
Cast 
Steel. 

Mitis 
Iron. 

Cast  Iron 
containing 
6.5  %  of 
Aluminum. 

Cast  Iron 
(ordinary). 

Air, 
(=.3133X&"). 

2,500 

1.2 

2 

2.5 

7 

9 

783 

5,000 

1.7 

2. 

3.4 

9.6 

13 

1,566 

7,500 

2.1 

3.4 

4 

11.6 

16 

2,350 

10,000 

2.2 

3.7 

4.4 

13.5 

18.5 

3,133 

12,500 

2.4 

4 

4.8 

15.7 

21.3 

3,916 

15,000 

2.7 

4.3 

5.2 

18.2 

24.1 

4,700 

17,500 

3.1 

4.6 

5.6 

21 

27.1 

5,483 

20,000 

3.5 

5 

6 

24 

30.5 

6,266 

22,500 

4 

5.4 

6.5 

27.2 

34.5 

7,050 

25,000 

4.5 

5.8 

7 

31 

39 

7,833 

27,500 

5 

6.2 

7.5 

35.5 

44 

8,616 

30,000 

5.5 

6.6 

8.1 

41.5 

50       » 

9,400 

32,500 

6 

7.1 

8.7 

47.5 

57 

10,163 

35,000 

6.5 

7.6 

9.4 

54 

65 

10,966 

37,500 

7 

8.2 

10.1 

62 

76 

11,750 

40,000 

7.5 

8.8 

10.9 

72 

88 

12,532 

42,500 

8 

9.4 

11.7 

83 

101 

13,315 

45,000 

8.5 

10.1 

12.6 

95 

116 

14,100 

47,500 

9 

10.9 

13.6 

110 

136 

14,882 

50,000 

9.6 

11.8 

14.7 

128 

160 

15,665 

52,500 

10.3 

12.8 

15.9 

149 

189 

16,450 

55,000 

11.1 

13.9 

17.3 

173 

222 

17,233 

57,500 

12 

15.1 

19 

200 

257 

18,016 

60000 

13 

16.4 

21 

230 

295 

18,800 

62,500 

14.2 

17.8 

23.2 

263 

340 

65,000 

15.7 

19.3 

25.6 

300 

400 

67,500 

17.5 

20.9 

28.5 

345 

470 

.  . 

70,000 

19.6 

22.7 

32 

400 

570 

.  . 

72,500 

22 

24.7 

36 

460 

700 

75,000 

24.7 

27 

41 

525 

77,500 

27.7 

30 

47 

600 

.  . 

80,000 

31.2 

34 

54 

700 

82,500 

35.2 

39 

62 

t 

85,000 

39.7 

44 

70 

.  . 

87,500 

44.7 

50 

80 

.  . 

90,000 

50.7 

57 

92 

t 

.  . 

92,500 

58 

65 

109 

.  . 

95.000 

67 

75 

131 

97,500 

78 

86 

159 

.  . 

100,000 

91 

100 

193 

102,500 

108 

121 

245 

.  . 

105,000 

137 

159 

290 

.  . 

107,500 

190 

227 

345 

,  . 

110,000 

290 

325 

410 

112,500 

395 

430 

500 

. 

.  . 

115,000 

500 

550 

600 

.  . 

117,500 

600 

650 

700 

. 

120,000 

700 

750 

800 

.  . 

122,500 

800 

850 

.  . 

.  . 

125,000 

900 

950 

•  • 

§88] 


THEORY  OF    THE  MAGNETIC   CIRCUIT. 


337 


curve,  by  actually  testing  the  very  iron  he  is  going  to  use  for 
his  machine. 


TABLE    LXXXIX. — SPECIFIC    MAGNETIZING    FORCES   FOR   VARIOUS 
MATERIALS  AT  DIFFERENT  DENSITIES,  IN  METRIC  MEASURE. 


UNIT  MAGNETIZING  FORCE. 

MAGNETIC 

AMPERE-TURNS  PER  CENTIMETRE  LENGTH. 

DENSITY. 

Lines  of  Force 

Air 

per  cm2 

<B 

Annealed 
Wrought 
Iron. 

Soft 
Cast 
Steel, 

Mitis 
Iron. 

Cast  Iron 
containing 
6.5  %  of 
Aluminum 

Cast 
Iron 
(Ordinary) 

AJft| 

(-£*•) 

500 

.5 

.9 

1.1 

3 

5 

400 

1.000 

.8 

1.25 

1.5 

4 

6 

800 

1,500 

.9 

1.45 

1.7 

5 

7 

1,200 

2,000 

.95 

1.6 

1.9 

6.5 

8.5 

1,600 

2,500 

1.1 

1.75 

2.1 

8 

10 

2,000 

3,000 

1.35 

1.95 

2.3 

9.5 

12 

2,400 

3,500 

1.6 

2.15 

2.6 

11 

14 

2,800 

4,000 

1.8 

2.35 

2.8 

13 

16 

3,200 

4.AOO 

2.1 

2.55 

3.1 

15 

19 

3,600 

5,000 

2.35 

2.8 

34 

19 

22 

4,000 

5,500 

2.6 

3.05 

3.7 

22.5 

26 

4,400 

6,000 

2.85 

335 

4.1 

26.5 

32 

4,800 

6,500 

3.1 

365 

4.5 

31.5 

38 

5,200 

7,000 

3.35 

4 

5 

37.5 

46 

5,600 

7,500 

3.6 

4.4 

5.5 

45 

57 

6,000 

8,000 

3.95 

4.9 

6.1 

56 

71 

6,400 

8,500 

4.35 

5.5 

6.75 

68 

87 

6,800 

9,000 

4.8 

6.0 

7.6 

81 

105 

7,200 

9,500 

5.4 

6.7 

8.7 

99 

125 

7,600 

10,000 

6.1 

7.5 

10.0 

118 

153 

8,000 

10,500 

7 

8.3 

11.5 

138      . 

190 

.  . 

11,000 

8 

92 

13.5 

163 

240 

11.500 

9.4 

10.3 

16 

195 

12,000 

10.8 

11.7 

18.5 

235 

. 

12,500 

12 

14 

22 

285 

13,000 

15 

16 

26 

.  . 

13,500 

17 

20 

30.5 

. 

, 

14,000 

20 

23 

37 

14,500 

24 

27 

46 

.  . 

15,000 

30 

32 

58 

. 

.  . 

15,500 

36           40 

74 

. 

. 

.  . 

16,000 

47 

52 

96 

.  . 

16,500 

68 

80 

124 

. 

17,000 

108          124 

160 

. 

17,500 

160          176 

204 

18,000 

212          228 

250 

.  . 

.  . 

18,500 

264        ;  280 

300 

.  . 

19,000 

316          333 

350 

19,500 

368 

386 

400 

.  . 

20,000 

420 

440 

450 

338 


DYNAMO-ELECTRIC  MACHINES. 


[$88 


MAGNETIC  DENSITY.  IN   LINES  OF  FORCE  PER  SQUARE  INCH 


IS 

era' 
to 

ox 

<> 

"I 

C/2 


3 
Is- 


</:  -o 
t— i  R 
^  3D 


O  -^ 
S  D 
'  H 

I 


|J 


1  I  I  1  I  i  I  1  ! 

MAGNETIC  DENSITY,  IN  LINES  OF  FORCE  PER  SQUARE  CENTIMETRE 


» 


CHAPTER  XVIII. 

MAGNETIZING    FORCES. 

89.  Total  Magnetizing  Force  of  Machine. 

The  total  exciting  power  required  for  a  dynamo-electric 
machine  is  the  sum  of  the  magnetizing  forces  needed  to  over- 
come the  reluctances  due  to  the  gap-spaces,  to  the  armature 
core,  and  to  the  field  frame,  and  of  the  magnetizing  force 
required  to  compensate  the  reaction  of  the  armature  winding 
upon  the  magnetic  field: 

AT=atg  +  at.  +  atm  X  atr,       (227) 

where    AT  —  total   magnetizing   force  required    for    normal 

output  of  machine,  in  ampere-turns; 
atg     —  ampere-turns  needed  to    overcome  reluctance 

of  gap-spaces;  see  formula  (228),  §  90; 
at^     =  ampere-turns  needed   to  overcome  reluctance 

of  armature  core;  see  formula  (230),  §  91; 
atm    —  ampere-turns   needed  to  overcome  reluctance 

of  magnet  frame;  see  formula  (238),  §  92; 
atr     =  ampere-turns  needed  to  compensate  armature 

reactions;  see  formula  (250),  §  93. 

90.  Ampere-Turns  for  Air  Gaps. 

The  magnetizing  force  required  to  produce  a  magnetic 
density  of  3C"  lines  of  force  per  square  inch  in  the  air  spaces, 
according  to  §  88,  is: 

atg  =  —  X  3C"  X  -^_  =  .3133  X  3C"  X  /"g,      (228) 
4  ft  2'54 

where  3C"  =    field  density,  in  lines  of  force  per  square  inch; 
from  formula  (142),  §  57,  for  smooth  armature 

0 

dynamos,  and  from  -^-  for  machines  with  toothed 

^« 

and  perforated  armatures,  the  area  of  the  clear- 
ance spaces,  S'g ,  to  be  taken  from  the  numer- 
ators of  equations  (174)  to  (176),  respectively, 
§64; 

339 


340  DYNAMO-ELECTRIC  MACHINES.  [§91 

/"g  =  length  of  magnetic  circuit  in  air  gaps,  inches; 
see  formula  (166),  §  64,  for  smooth  armatures, 
and  denominators  of  (174)  to  (176)  for  toothed 
and  perforated  armatures,  respectively. 

If  the  field  density  is  given  in  lines  of  force  per  square  cen- 
timetre, and  the  length  of  the  circuit  in  centimetres,  the  mag- 
netizing force  in  ampere-turns  is  obtained  from 

at^  —  ~   -  X  OC  X  lg  =  .  796  X  3C  x  /g  , 
4  ft 

or,  approximately: 

afg=   .8  X  OC  X  /g, 


91.  Ampere-Turns  for  Armature  Core. 

For  the  magnetizing  force  needed  to  overcome  the  reluctance 
of  the  armature  core  we  find,  according  to  formula  (226): 

«>a=/((**a)    X    /"a,         ..........  (230) 

where/  (&"a)  =  average  specific  magnetizing  force,  in  ampere- 
turns    per   inch   length,    formulae  (231)    to 

(235); 

l"&  =  mean  length  of  magnetic  circuit  in  armature 
core  in  inches,  formula  (236)  or  (237), 
respectively. 

Owing  to  the  circular  shape  of  the  armature  the  area  of  the 
surfaces  presented  to  the  lines  when  entering  and  leaving  the 
core  is  much  greater  than  that  of  the  actual  cross-section  of 
the  armature  body.  Hence,  since  every  useful  line  of  force, 
on  its  way  from  a  north  pole  to  the  adjoining  south  pole,  must 
pass  through  the  smallest  core  section,  it  is  evident  that  the 
magnetizing  force  required  per  unit  of  path  length  is  smallest 
near  the  polepieces  and  greatest  opposite  the  neutral  points  of 
the  field,  while  it  gradually  increases  from  the  minimum  to  the 
maximum  value  as  the  flux  passes  from  the  peripheral  surface 
opposite  the  north  pole  to  the  neutral  cross-section,  and  grad- 
ually decreases  again  to  minimum  as  the  flux  proceeds  from 
the  neutral  section  to  the  periphery  opposite  the  south  pole. 


§91]  MAGNETIZING  FORCES.  34* 

The  average  specific  magnetizing  force,  therefore,  is  obtained 
by  taking  the  arithmetical  mean  of  the  extreme  values^  __ 


/(«'.)  =  7  {/(«'.,)+/(«'„)  } 


in  which/  ((&"ai)  =  maximum    specific   magnetizing   force,  for 

smallest  area   of   magnetic   circuit;   see 

Table  LXXXVIII.,  column  for  annealed 

wrought  iron; 
f  (®'a2)  —  maximum  specific   magnetizing  force,  for 

largest  area  of  magnetic  circuit,    Table 

LXXXVIII.  ; 

3>  =  useful  flux  of  machine,  in  webers; 

S"&1         —  net   cross-section    of    armature    core,    in 

square  inches; 
*S"aa         =  maximum  area  of  circuit  in  armature  core, 

in  square  inches. 

The  area  of  the  magnetic  circuit  in  the  armature  can  be 
expressed  by  the  product  of  the  net  length  and  the  depth  of 
the  core,  and  of  the  number  of  poles;  hence  the  minimum 
area: 

S"ai  =  2  n    X  4  X  b&  X  * 


and  the  maximum  area: 

S"a2  =  2npx  4  x  b\  x  k^     ......  (233) 

where  nv    =  number  of  pairs  of  magnet  poles; 
/a      =  length  of  armature  core,  in  inches; 
b&     —  radial  depth  of  armature  core,  in  inches; 
b  a    =  maximum  depth  of  armature  core,  in  inches; 
k^     =  ratio  of  net  iron  section  to  total  cross-section  of 
armature  core,  see  Table  XXIII.,  §  26. 

In  multipolar  dynamos  the  maximum  depth  b'&  of  the  core 
is  approximately  equal  to  half  the  tangential  width  of  the  pole- 
pieces;  for  bipolar  machines  b'&  is  half  the  largest  chord  that 
can  be  drawn  between  the  internal  and  external  armature  per- 
ipheries. For  bipolar  smooth  armatures,  Fig.  257,  b\  can  be 


342 


DYNAMO-ELECTRIC  MACHINES. 


91 


expressed  by  the  core  diameter,  </a,  and  the  radial  depth,  £a,  as 
follows: 


Fig.  257. — Maximum  Core-Depth  in  Bipolar  Smooth  Armature. 

^  =  y/^^+Y'-^^- 

F~: (284) 

And  for  bipolar  toothed  and  perforated  armatures,  with  refer- 
ence to  Fig.  258,  we  have: 


Fig.  258. — Maximum  Core-Depth  in  Bipolar  Toothed  Armature. 


rV   -~   d  V  +  4  ^*a    X    (^a  +  ^a)  —  4  (^a  +  ^a)" 

4 


(235) 


§91] 


MAGNETIZING  FORCES. 


343 


The  path  of  the  magnetic  circuit  through  a  smooth  armature 
core  is  illustrated  in  Fig.  259,  from  which  it  is  evident _that 
the  length  l"&  can  be  expressed  by: 


Fig.  259. — Length  of  Magnetic  Path  in  Smooth  Armature  Core. 


,(236) 


In  case  of  toothed  and  perforated  armatures,   Fig.  260,   the 
length  of  the  path  is: 


Fig.  260.—  Length  of  Magnetic  Path  m  Toothed  Armature  Core. 


...  (237) 


where  d'"&  •=  mean  diameter  of  armature  core,  in  inches; 
b&     •=  radial  depth  of  armature  core,  in  inches; 
//a    =  depth  of  armature  slots,  in  inches; 
«p    =  number  of  pairs  of  magnet  poles; 
a     =  half  angle  between  adjacent  pole  corners. 


344  DYNAMO-ELECTRIC  MACHINES.  [§92 

92.  Ampere-Turns  for  Field  Magnet  Frame. 

Taking  the  most  general  case  of  a  magnet-frame  consist- 
ing of  three  different  materials  —  wrought-iron  cores,  cast-iron 
yokes,  and  steel  polepieces—  then,  according  to  (226)  we 


obtain: 

)  X  /» 


X/8,      ..(238) 

where  (B"w  L,  (B"c>i.,  (B"s  =   magnetic  densities  in  wrought  iron, 

cast    iron,  and    in    steel,  respec- 
tively, in  lines  per  square  inch; 

/(®"w.i.),  /  (®"c.i.),  /  \®>"s)  =   corresponding    specific   magnet- 

izing   forces    of     the     respec- 
tive    materials,      from     Table 
LXXXVIIL,  or  Fig.   256; 
X  /Vi  ^/ci.    X  ///i(B//     X  /'. 


=  average  specific  magnetizing  force  of  magnet  frame 

in  ampere-turns  per  inch  length; 

/"w.i.,  ^"c.i.,  /*s  —  lengths  of  magnetic  circuit  in  wrought  iron, 

in  cast  iron,  and  in  steel,  respectively,  in  inches; 

/"m  =  7"w  h  4-  /"c>i  -f  /*g  =  total    length  of  magnetic  circuit  in 

magnet  frame,  in  inches. 

The  densities  (Bvv-i.,  (BC.L,  and  (Bs  are  the  quotients  of  the  total 
magnetic  flux,  #',-by  the  mean  total  areas,  *S*W-1.,  *S"*Cil.,  and  ^"g, 
of  the  magnetic  circuits  in  the  respective  materials: 

«",,,.  =  1^-;  «",,.=  %-;  «'.  =  J  .....  (239) 

*J  w.i.  °  c.i.  °  s 

If  two  or  more  portions  of  the  frame  are  made  of  the  same 
material,  but  of  different  cross-sections,  either  each  of  these 
portions  has  to  be  treated  separately,  or  their  average  specific 
magnetizing  force  must  be  found,  exactly  as  in  the  case  of  dif- 
ferent materials.  Thus,  if  the  path  in  a  certain  material,  for 
some  mechanical  or  constructive  reason,  has  different  sectional 
areas,  Slt  S^  6"3,  ----  in  various  portions,  /„  /2,  /3,  ----  of  its 
length,  the  total  magnetizing  force  required  for  that  mate- 
rial is: 


§92] 


MAGNETIZING  FORCES. 


345 


7T  )  X  /.  + 


(240) 


where 


/ 


/<p'\  = 


-  IX 


Since  the  resultant  area,  6",  in  this  formula  is  different 
the  arithmetical  as  well  as  from  the  geometrical  mean  of  the 


single  areas,   *$*, 


the  use  of  either  of  these  mean 


areas  would  lead  to  an  incorrect  result.  And  since,  further- 
more, the  specific  magnetizing  force  does  not  vary  in  direct 
proportion  with  the  flux-density,  it  would  also  be  a  fallacy  to 
use  the  specific  magnetizing  force  corresponding  to  the  aver- 
age density  computed  from  the  separate  densities, 


V  •%' 


by  taking  their  arithmetical  or  even  their  geometrical  mean. 

Similarly,  if  the  area  presented  to  the  lines  of  force  is  not 
uniform  throughout  the  length  of  their  path  in  a  certain  por- 


Figs.  261  to  263. — Polepieces  with  Gradually  Increasing  Sectional  Area. 

tion  of  the  field  frame,  neither  the  mean  area  nor  the  mean  flux 
density,  obtained  by  averaging  the  respective  extreme  values, 
should  be  used,  but  the  specific  magnetizing  force  for  the  max- 
imum and  minimum  cross-section  must  be  calculated,  and 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§92 


either  their  arithmetical  or  their  geometrical  mean  be  taken, 
according  to  whether  the  variation  in  cross-section  is  a  con- 
tinual or  a  non-gradual  one.  The  sectional  areas  of  the  magnet 
cores  and  of  they06esin  most  cases  are  uniform  throughout  their 
respective  lengths;  but  the  cross-section  of  the  polepieces,  owing 
to  their  peculiar  shape,  usually  varies  along  their  length.  In 
case  the  sectional  area  gradually  rises  from  a  minimum  near 
the  core  to  a  maximum  at  the  poleface,  as  in  Figs.  261,  262, 
and  263,  the  average  specific  magnetizing  force  is  the  arith- 
metical mean  of  the  extreme  values: 


in  which  /  ((B"p)  =  average  specific  magnetizing  force  of  pole- 
piece,  in  ampere-turns  per  inch; 

St  =  cross-section  of  polepieces  near  magnet- 
core  (or  twice  the  minimum  cross-section 
at  center  of  polepiece,  Fig.  262),  in 
square  inches; 

S9  =  Pole  face  area  (maximum  cross-section  of 
polepiece),  in  square  inches. 

If,  on  the  other  hand,  the  area  is  partly  uniform  and  partly 
varying,  as  in  the  polepieces  shown  in  Figs.  264  and  265,  the 
geometrical  mean  of  the  specific  magnetizing  force  of  the 
uniform  portion  and  of  the  average  specific  magnetizing  force 
of  the  varying  portion  has  to  be  taken  as  follows: 


Figs.  264  and  265. — Polepieces  with  Partly  Uniform  and  Partly  Varying  Cross-- 
Section. 


/(«•»)= 


(242) 


§92] 


MAGNETIZING  FORCES. 


347 


where  St  =  area  of '  uniform   cross-section    (minimum    cross- 
section),  in  square  inches; 
£2  =  pole  face  area  (maximum  cross-section),  in  square 

inches; 

/j    =  length  of  uniform  cross-section,  in  inches; 
/2    =  mean  length  of  varying  cross-section,  in  inches. 

In  formulae  (241)  and  (242)  it  is  assumed  that  the  smallest  sec- 
tion of  the  polepiece  is  entered  by  the  entire  total  flux,  $', 
and  that  the  pole  area  only  carries  the  useful  flux,  0.  Neither 


Figs.  266  and  267. — Mean  Length  of  Magnetic  Circuit  in  Cores  and  Yokes. 

of  these  assumptions  is  quite  correct  (the  number  of  lines 
entering  the  polepieces  being  smaller  than  $',  and  the  flux  at 
the  pole  face  somewhat  larger  than  <&)  but,  since  their  devia- 
tions from  the  facts  are  in  opposite  directions,  they  practically 
cancel  in  forming  the  arithmetical  mean  of  the  respective 
specific  magneting  forces  and  give  a  result  as  accurate  as  can 
be  desired. 

The  mean  length  of  the  magnetic  circuit  in  portions  of  the 
field  frame  having  a  homogenous  cross-section  (cores  and  yokes] 
is  measured  along  the  centre  line  of  the  frame,  as  shown  in 
Fig.  266,  if  there  is  but  one  magnetic  circuit  through  that  por- 
tion. In  case  of  two  or  more  magnetic  circuits  passing  in 
parallel  through  any  part  of  the  frame,  as  in  Fig.  267,  that 
part  is  to  be  correspondingly  subdivided  parallel  with  the 
direction  of  the  magnetic  lines,  and  the  mean  length  of  the 
magnetic  circuit,  then,  is  given  by  the  centre-line  through  a 
part  of  the  frame  thus  apportioned  to  one  circuit.  In  the 
illustration,  Fig.  267,  two  parallel  circuits  being  shown  through 
each  core,  the  average  line  of  force  passes  through  the  cores 
at  a  distance  from  their  edges  equal  to  one-quarter  of  their 
breadth. 


348 


DYNAMO-ELECTRIC  MACHINES. 


[§93 


In  parts  with  varying  cross-section  (polepieces)  the  mean 
length  of  the  magnetic  circuit,  depending  altogether  upon 
their  shape,  can  only  be  estimated,  one  approximation  being 


Figs.  268  and  269.  —  Mean  Length  of  Magnetic  Circuit  in  Polepieces. 

the  arithmetical  mean  between  the  shortest  and  the  longest 
line  of  force  (see  Figs.  268  and  269): 


/"p  =  mean  length  of  magnetic  circuit  in  polepieces,  in 

inches; 

/x    =  shortest  line  of  force  in  polepiece; 
/a    =  longest  line  of  force  in  polepiece. 

93.   Ampere-Turns   for    Compensating    Armature   Re- 
actions. 

The  armature  current  in  magnetizing  the  armature  core 
exerts  a  double  influence  upon  the  magnetic  circuit:  (i)  a 
direct  weakening  influence  upon  the  magnetic  field,  due  to  the 
lines  of  force  set  up  by  the  armature  winding,  and  (2)  an  indi- 
rect, secondary  influence  by  shifting  the  magnetic  field  in  the 
direction  of  the  rotation,  thereby  causing  greater  magnetic 
density  to  take  place  in  those  portions  of  the  polepieces  at 
which  the  armature  leaves  the  pole  than  in  those  at  which  it 
enters. 

The  direct  effect  of  the  ampere-turns  upon  the  field  has  been 
studied  experimentally  by  Professor  Harris  J.  Ryan,1  who,  in 
his  paper  presented  to  the  American  Institute  of  Electrical 
Engineers,  on  September  22,  1891,  has  shown  that  the  arma- 


1  Harris  J.  Ryan,  Trans.  A.  7.  E.  E.,  vol.  viii.  p.  451  (September  22,  1891); 
Electrical  Engineer,  vol.  xii.  pp.  377,  404  (September  30  and  October  7,  1891); 
Electrical  World,  vol.  xvii.  p.  252  (October  3,  1891). 


§93]  MAGNETIZING  FORCES.  349 

ture  ampere-turns   acting   directly  against   the   field  ampere 
turns  can  be  expressed  by: 


180 


where  at'r  =  counter  magnetizing  force  of  armature  per  mag- 
netic circuit,   in  ampere-turns,  to  be  compen- 
sated for  by  additional  windings  on  field  frame; 
N&  =  total  number  of  turns  on  armature, 
N&  =  Nc ,  for  ring  armatures, 
jVa  =  J.  jVc,  for  drum-wound  armatures, 
(Nc  =  total  number  of  armature  conductors); 
/'  —  total  current-capacity  of  dynamo,  in  amperes; 
2n'p  =  number  of  armature  circuits  electrically  connected 
in  parallel; 

N  X  /' 

—, —  =  total  number  of  ampere-turns  on  armature; 

£ia  x  a  =  angle  of  brush  lead. 

For  smooth-core  armatures  the  angle  of  lead  is  approximately 
equal  to  half  the  angle  between  two  adjacent  pole  corners,  the 
constant  >&13  being  very  nearly  =  i,  and  is  accurately  expressed 
by  formula  (245).  , 

Since  the  angle  of  field-distortion  depends  upon  the  relative 
magnitudes  of  the  armature-  and  field  magnetomotive  forces 
acting  at  right  angles  to  each  other,  the  direction  of  the  dis- 
torted field  is  the  resultant  of  both  forces;  that  is,  the  diag- 
onal of  a  rectangle,  having  the  two  determining  M.  M.  Fs. 
as  its  sides,  as  shown  in  Fig.  270,  in  which  OA  represents  the 
direction  and  magnitude  of  the  direct  M.  M.  F.,  and  OB 
that  of  the  counter  M.  M.  F.  The  angle  of  lead  can,  con- 
sequently, be  mathematically  expressed  by: 

_  OB  _  Total  Armature  Ampere-Turns 
OA  Total  Field  Ampere-Turns 

N    X  I' 

~  nz  X  AT  =  2»'p  X  nz  X  AT  ' 
or 

a  =  arc  tan 


35° 


DYNAMO-ELECTRIC  MACHINES. 


[§93 


the  total  number  of  field  ampere-turns  being  the  product  of  the 
number,  AT,  of  ampere-turns  per  magnetic  circuit,  and  of  the 
number,  «2,  of  magnetic  circuits. 

In  toothed  and  perforated  machines  the  weakening  effect  of  the 
armature  magnetomotive  force  is  checked  by  the  presence  of 
iron  surrounding  the  conductors,  this  checking  influence  being 
the  stronger  the  greater  the  ratio  of  tooth  section  to  field  den- 
sity, that  is,  the  smaller  the  tooth  density.  In  a  minor  degree, 
the  coefficient  of  brush  lead  depends  upon  the  ratio  of  gap 
length  to  pitch  of  slots,  and  upon  the  peripheral  velocity  of  the 
armature.  In  the  following  Table  XC.  averages  for  this  co- 
efficient, /&13 ,  for  toothed  and  perforated  armatures  are  given, 
the  upper  limits  referring  to  small  gaps  and  high-speed  arma- 
tures, and  the  smaller  values  to  large  air  gaps  and  to  armatures 
of  low  circumferential  velocity: 

TABLE    XC. — COEFFICIENT   OF   BRUSH   LEAD  IN   TOOTHED   AND   PER- 
FORATED ARMATURES. 


MAXIMUM  DENSITY 
OP  MAGNETIC  LINES 
IN  ARMATURE  PROJECTIONS 
AT  NORMAL  LOAD. 

COEFFICIENT  OF  BRUSH  LEAD, 

*„ 

Toothed  Armatures. 

Perforated 
Armatures. 

Lines  per  sq.  in.  ILinesper  sq.  cm. 

Straight  Teeth. 

Projecting  Teeth. 

50,000 
75,000 
100,000 
125,000 
150,000 

7,750 
11,600 
15,500 
19,400 
23,250 

0.30  to  0.45 
.35"     .60 
.40  "     .80 
.50  "     .90 
.70  "  1.00 

0.25  to  0.35 
.30  "     .45 
.40  "     .60 
.50"     .70 
.60  "     .90 

0.20  to  0.30 
.25  "  .35 
.30  "  .45 
.40  "  .60 
.50  "  .80 

Formula  (244)  is  directly  applicable  to  single  magnetic  circuit 
bipolar  and  to  the  radial  types  of  imtltipolar  machines.  In  double 
circuit  bipolar  types,  and  for  axial  multipolar  dynamos,  however, 
in  which  the  number  of  magnetic  circuits  per  pole  space  is 
twice  that  of  the  former  machines,  respectively,  the  result  of 
(244),  must  be  divided  by  2  in  order  to  furnish  the  direct  counter 
magnetizing  force  per  magnetic  circuit. 

As  to  the  second,  indirect,  influence  of  the  armature  field,  the 
density  in  the  Sections  I,  I,  Fig.  270,  of  the  polepieces,  on 
account  of  the  distortion  of  the  field  caused  by  the  action  of 
the  armature  current,  is  greater,  in  the  Sections  II,  II,  how- 


§93] 


MAGNETIZING  FORCES. 


351 


ever,  smaller  than  the  average  density  obtained  by  dividing 
the  total  flux  by  the  sectional  area  of  the  polepieces. 


Fig.  270.  —  Influence  of  Armature  Current  upon  Magnetic  Density  in  Polepieces. 

If  the  average  density  in  the  polepieces,  $'  -+•  Sp,  is  denoted 
by  (fc"p,  then  the  distorted  densities  are 


in   Sections  I,    I:      (B"pl  =  &"p  X 


i  —  sin  a 
in  Sections  II,  II:  &"pn  =  ®"P  X          ^7- 


(246) 


The  magnetizing  force  required  to  produce  these  densities 
in  the  polepieces  can  be  found  from 

af       p       /(«'»)+/«»',.),     ....(247) 

2 

where  /"p  =  length  of  magnetic  circuit  in  the   polepieces,  in 

inches; 

/  (®V)  and  /  (®"pn)  =  specific  magnetizing  forces  per 
inch  length  for  the  densities  (B"pl  and  (B"pII ,  re- 
spectively, formula  (245),  for  the  material  used; 
to  be  taken  from  Table  LXXXVI.,  or  from  Fig. 
256. 

But  since  the  magnetic  force  necessary  to  produce  the  origi- 
nal average  density  is 

*'p=>PX/((B*p), 

which  is  smaller  than  at'^  we  can  find  the  number  of  ampere- 
turns  by  which  the  field  magnetomotive  force  is  diminished  on 
account  of  this  indirect  effect  of  the  armature  current,  by  sub- 
tracting atp  from  (247).     Doing  this  we  obtain: 
afr  =  at'p  -  atv 


352 


DYNAMO-ELECTRIC  MACHINES. 


[§93 


The  total  weakening  effect  of  the  armature  winding  per  mag- 
netic circuit  can  therefore  be  found  by  combining  (244)  and 
(248),  thus: 

at- =  aSf  +  of. 


271 


X 


l8o° 


.(249) 


This  is  the  total  number  of  ampere-turns  by  the  amount  of 
which  the  exciting  power  of  each  magnetic  circuit  is  to  be  in- 
creased in  order  to  compensate  for  the  reactions  of  the  arma- 
ture current  upon  the  field. 

Making  the  above  calculation  of  atr,  by  formula  (249),  for  a 
great  number  of  practical  machines,  the  author  has  found  that 
with  sufficient  accuracy  the  complex  formula  (249)  can  be  re- 
placed by  the  simple  equation: 


i8ol 


(250) 


if  the  following  values  of  the  coefficient  /£14  are  employed : 

TABLE    XCI.  —COEFFICIENT    OF   ARMATURE    REACTION    FOR   VARIOUS 
DENSITIES  AND  DIFFERENT  MATERIALS. 


AVEBAGE  MAGNETIC  DENSITY 

IN  POLEPIECES. 

Wrought  Iron 
and  Cast  Steel. 

Mitis*  Iron. 

Cast  Iron. 

Coefficient 
of 
Armature 

Lines 

Lines 

Lines 

Lines 

Lines 

Lines 

Reaction 

per  sq.  in. 

per  sq.  cm. 
<Bp 

per  sq.  in. 

per  sq.  cm. 

(B  p 

per  sq.  cm. 
(Bp 

*„ 

80,000* 

12,400* 

.25 

90,000 

13,950 

70,'doo* 

10,850* 

.... 

.... 

.30 

100,000 

15,500 

80,000 

12,400 

.... 

.... 

.40 

105,000 

16,250 

90,000 

13,950 

20,000* 

3,100* 

.50 

110,000 

17,000 

100,000 

15,500 

30,000 

4,650 

.60 

115,000 

17,800 

105,000 

16,250 

40,000 

6,200 

.70 

120,000 

18,600 

110,000 

17,000 

50,000 

7,750 

1.80 

.... 

115,000 

17,800 

55,000 

8,500 

1.90 

120,000 

18,600 

60,000 

9,300 

2.00 

.... 

.... 

.... 

65,000 

10,100 

2.10 





... 



70,000 

10,850 

2.25 

*  Or  lese. 


§94]  MAGNETIZING  FORCES.  353 

94.  Grouping  of  Magnetic  Circuits  in  Tarious  Types  of 
Dynamos. 

In  applying  formula  (227),  §  89,  for  the  total  magnetizing 
power  of  a  dynamo,  the  number  of  the  magnetic  circuits  and 
their  grouping  has  to  be  taken  into  account. 

Considering  each  magnet,  or  each  group  of  magnet  coils 
wound  upon  the  same  core,  as  a  separate  source  of  M.  M.  F., 
we  can  classify  the  various  types  of  dynamos  according  to  the 
number  of  sources  of  magnetomotive  force,  and  according  to 
their  grouping,  as  follows: 

(1)  One  source  of  M.  M.  F.,   single  circuit,   Figs.   271 

and  272; 

(2)  One  source  of  M.  M.  F.,  double  circuit,   Figs.   273 

and  274; 

(3)  One  source  of  M.  M.  F.,  multiple  circuit,  Figs.  275 

and  276; 

(4)  Two  sources  of  M.  M.  F.  in  series,   single  circuit. 

Figs.  277  and  278; 

(5)  Two  sources  of  M.  M.  F.  in  series,  double  circuit, 

Figs.  279  and  280; 

(6)  Two  sources  of  M.  M.  F.  in  parallel,  single  circuit, 
>  Figs.  281  and  282; 

(7)  Two  sources  of  M.  M.  F.  in  parallel,  double  circuit,. 

Figs.  283  and  284; 

(8)  Two  sources   of  M.  M.  F.  in  parallel,   multiple  cir- 

cuit, Figs.  285  and  286; 

(9)  Two  sources  of  M.  M.  F.  in  series,  each  also  sup- 

plying a  shunt  circuit,  Figs.  287  and  288; 
(10)  Three   or  more   sources  of  M.   M.   F.   in   parallel* 

multiple  circuit,  Figs.  289  and  290; 
(n)  Three  or  more  sources  of  M.  M.  F.  in  series,  each 

having  a  shunt  circuit,  Figs.  291  and  292; 

(12)  Four  sources  of  M.  M.  F.,  two  in  series  and  two  in 

parallel,  single  circuit,  Figs.  293  and  294; 

(13)  Four  sources  of  M.  M.  F.    in  series,  each  pair  also- 

supplying  a  shunt  circuit,  Figs.  295  and  296; 

(14)  Four  or  more  sources  of  M.  M.  F.  in  series,  paral- 

lel,  two  sources  in  series  in  each  circuit,    Figs. 
297  and  298; 


354 


DYNAMO-ELECTRIC  MACHINES. 


[§94 


(15)  Four  or  more  sources  of  M.  M.  F.,  all  in  parallel, 

multiple  circuit,  Figs.  "299  and  300; 

(16)  Four  or  more  sources  of  M.  M.  F.,  arranged  in  one 

or  more  parallel  branches  in  each  of  which  two 
separate  sources  are  placed  in  series  with  a  group 
of  two  in  parallel,  Figs.  301,  302  and  303. 

In  order  to  facilitate  the  conception  of  the  grouping  of  the 
magnetomotive  forces,  to  the  following  illustrations  of  the  16 
classes  enumerated  above  the  electrical  analogues  of  corre- 
sponding grouping  of  E.  M.  Fs.  have  been  added: 


FIG.  271  F.G  .272 


Fiq.  275  FIG..  2?6  FIG.  277  F'G.  278 

I 


FIG.  285 


FIG.  286 


FIQ.  287    FIG.  288 


FIG.  289 


FIG.  290 


FIG.  291    FIG.  292 


FIG.  293    FIG.  294 


FIG.  295     FIG.  296 


FIG.  297 


FIG.  298 


FIG.  299      FIG.  300    FIG.  301   FIG.  302   FIG.  303 

\\- 


Figs.  271  to  303. — Grouping  of  Magnetic  Circuits  in  Various  Types  of  Dyna- 
mos, and  Electrical  Analogues. 

Of  the  first  class,  Fig.  271,  which  has  but  one  magnetic  cir- 
cuit, are  the  bipolar  single  magnet  types  shown  in  Figs.  191, 
192,  193  and  194. 

In  the  second  class,  Fig.  273,  there  are  two  parallel  magnetic 


§94].  MAGNETIZING  FORCES.  355 

circuits,  each  containing  the  entire  magnetizing  force;  of  this 
class  are  the  single  magnet  bipolar  iron-clad  types,  illustrated 
in  Figs.  204,  205  and  206. 

The  third  class,  Fig.  275,  has  as  many  magnetic  circuits  as 
there  are  pairs  of  magnet  poles,  and  each  circuit  contains  the 
entire  magnetizing  force;  the  single  magnet  multipolar  types, 
Figs.  214  and  215,  belong  to  this  class. 

The  fourth  class,  Fig.  277,  has  but  one  magnetic  circuit,  and 
is  represented  by  the  single  horseshoe  types,  Figs.  187  to  190, 
and  by  the  bipolar  double  magnet  types,  Figs.  195,  196 
and  198. 

In  the  fifth  class,  Fig.  279,  there  are  two  magnetic  circuits, 
each  of  which  contains  both  magnets;  the  bipolar  double  mag- 
net iron-clad  types  shown  in  Figs.  203  and  207  belong  to  this 
class. 

The  sixth  class,  Fig.  281,  has  also  two  magnetic  circuits,  but 
each  one  contains  only  one  magnet;  of  this  class  are  the 
bipolar  double  magnet  types  illustrated  in  Figs.  197,  199 
and  200. 

In  the  seventh  class,  Fig.  283,  there  are  four  parallel  mag- 
netic circuits,  each  of  which  contains  but  one  magnet;  the 
fourpolar  iron-clad  types,  Figs.  218,  219  and  220,  and  the 
fourpolar  double  magnet  type,  Fig.  223,  belong  to  this  class. 

In  the  eighth  class,  Fig.  285,  the  number  of  magnetic  cir- 
cuits is  equal  to  twice  the  number  of  poles,  opposite  pole  faces 
of  same  polarity  considered  as  one  pole,  and  each  circuit  con- 
tains one  magnet;  this  class  is  represented  by  the  double 
magnet  multipolar  type,  Fig.  216. 

The  ninth  class,  Fig.  287,  has  three  magnetic  circuits,  two 
of  which  contain  one  magnet  each,  while  the  third  one  con- 
tains both  the  magnets. 

In  the  tenth  class,  Fig.  289,  there  are  as  many  magnetic  cir- 
cuits as  there  are  poles,  two  circuits  passing  through  each 
magnet;  the  multipolar  iron-clad  type,  Fig.  217,  is  of  this 
class. 

The  eleventh  class,  Fig.  291,  has  one  more  circuit  than  there 
are  pairs  of  poles,  one  circuit  containing  all  the  magnets, 
while  all  the  rest  contain  but  one  magnet  each;  to  this  class 
belongs  the  multiple  horseshoe  type,  Fig.  222. 

In  the  twelfth  class,  Fig.  293,  there  are  two  magnetic  cir- 


356  DYNAMO-ELECTRIC  MACHINES.  «[§  94 

cuits,  each  containing  two  magnets;  it  is  represented  by  the 
double  horseshoe  types,  Figs.  201  and  202. 

Class  thirteen,  Fig.  295,  has  three  circuits,  two  containing 
two  magnets  each  and  the  third  one  all  four  magnets;  to  this 
class  belongs  the  fourpolar  horseshoe  type,  Fig.  221. 

In  class  fourteen,  Fig.  297,  there  are  as  many  circuits  as 
there  are  poles,  each  circuit  containing  two  magnetomotive 
forces  in  series;  this  class  of  grouping  is  common  to  the  radial 
multipolar  types,  Figs.  208  and  209,  and  to  the  axial  multipolar 
type,  Fig.  212. 

In  class  fifteen,  Fig.  299,  the  number  of  magnetic  circuits  is 
equal  to  the  number  of  poles,  and  each  circuit  contains  one 
magnet;  the  tangential  multipolar  types,  Figs.  210  and  211, 
and  the  quadruple  magnet  type,  Fig.  224,  are  the  varieties  of 
this  class. 

The  sixteenth  class,  Fig.  301,  finally,  has  as  many  magnetic 
circuits  as  there  are  poles,  and  each  circuit  contains  three 
magnets;  the  raditangent  multipolar  type  which  is  shown  in 
Fig.  213,  represents  this  class  of  grouping. 

Similarly  as  the  total  joint  E.  M.  F.  of  a  number  of  sources 
of  electricity  connected  in  series-parallel  is  the  sum  of  the 
E.  M.  Fs.  placed  in  series  in  any  of  the  parallel  branches,  so 
the  total  M.  M.  F.  of  a  dynamo-electric  machine  is  the  sum 
of  the  M.  M.  Fs.  in  series  in  any  of  its  magnetic  circuits. 

In  considering,  therefore,  one  single  magnetic  circuit  for 
the  computation  of  the  magnetizing  forces  required  for  over- 
coming the  reluctances  of  the  air  gaps,  armature  core  and 
field  frame,  the  result  obtained  by  formula  (227)  represents 
the  exciting  force  to  be  distributed  over  all  the  magnets  in 
that  one  circuit,  and,  consequently,  the  same  magnetizing  force 
is  to  be  applied  to  all  the  remaining  magnetic  circuits,  pro- 
vided all  circuits  contain  the  same  number  of  magnets. 

In  case  of  several  magnetic  circuits  with  a  different  number 
of  M.  M.  Fs.  in  series,  as  in  classes  9,  n  and  13,  which  have 
one  long  circuit  containing  all  the  magnets,  and  several  small 
circuits  with  but  one  or  two  magnets,  respectively,  the  total 
M.  M.  F.  of  the  machine  is  either  the  sum  of  all  M.  M.  Fs.  or 
the  joint  M.  M.  F.  of  one  of  the  small  circuits,  according  to 
whether  the  long,  or  one  of  the  small  circuits  has  been  used  in 
calculating  the  magnetizing  force  required  for  the  machine. 


PART  VI. 


CALCULATION  OF   MAGNET  WINDING. 


CHAPTER   XIX. 

COIL    WINDING    CALCULATIONS. 

95.  General  Formulae  for  Coil  Windings, 

In  practice  it  frequently  is  desired  to  make  calculations  con- 
cerning the  arrangement,  etc.,  of  magnet  windings,  without 
reference  to  their  magnetizing  forces;  and  it  is  for  the  simpli- 
fication of  such  computations  that  the  following  general  for- 
mulae for  coil  windings  are  compiled. 

In  Fig.  304  a  coil  bobbin  is  represented,  and  the  following 
symbols  are  used: 

Dm  =  external  diameter  of  coil  space,  in  inches; 

dm    —  internal  diameter  of  coil  space,  in  inches; 

/m    =  length  of  coil  space,  in  inches; 

hm   =  height  of  coil  space,  in  inches; 

Vm  —  volume  of  coil  space,  in  cubic  inches; 

3m  =  diameter  of  magnet  wire,  bare,  in  inches; 

6'm  =  diameter  of  magnet  wire,  insulated,  in  inches; 

Nm  =  total  number  of  convolutions; 

Zm  =  total  length  of  magnet  wire,  in  feet; 

wtm  —  total  weight  of  magnet  wire,  in  pounds; 

rm    =  resistance  of  magnet  wire,  in  ohms; 

pm   =  resistivity  of  magnet  wire,  in  ohms  per  foot; 

Am  =  -  -  =  specific  length  of  magnet  wire,  in  feet  per 

Pm 

ohm; 
A/m  =  specific  length  of  magnet  wire,  in  feet  per  pound. 

The  total  number  of  convolutions  filling  a  coil  space  of  given 
dimensions  with  a  wire  of  given  size  is: 

#*  =  •£?-  x  -fc  =  /m  £  f m (251) 

°  m  °  in  °  m 

359  ' 


36° 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§05 


The  diameter  (insulated)  of  wire  required  to  fill  a  bobbin  of 
given  size  with  a  given  number  of  convolutions,  irrespective 
of  resistance,  is: 

«S'm  =  J  L*  *- 


(252) 


Fig.  304. — Dimensions  of  Coil  Bobbin. 

The  total  length    of  wire  of  given  diameter  which  can   be 
wound  on  a  bobbin  of  given  dimensions,  is: 


D 


12 


7m  X 


=  .  ,6.x 


From  (254)  the  dimensions  of  a  coil  can  be  calculated  on 
which  a  certain  length  of  wire  of  given  diameter  can  be  wound. 

If  the  internal  diameter  and  the  height  of  the  coil  space  are 
given,  the  length  can  be  computed  from: 


/ 
~ 


12  x 


X 


X  n  X 


§95]  COIL    WINDING  CALCULATIONS.  361 

When  length  and   winding  depth  are  known,  the  internal 
coil  diameter  is  found  from: 

_  12  X  Zm  X  <?'m2  -  /C  X  /m  X  n 
4  X  hm  X  n 

js=3.82Xy^^    -^m (256) 

And  if  the  length  and  the  internal  diameter  of  the  coil  are 
given,  its  winding  depth  can  be  obtained  from: 


Since  the  length  of  a  wire  is  the  product  of  its  weight  and 
its  specific  length,  formula  (257)  can  be  modified  so  as  to  give 
the  height  of  the  coil  space  required  to  wind  a  given  weight  of 
wire  of  given  diameter  upon  a  core  of  known  dimensions: 


x*'-  +  4El_4«L.    (258) 


/m    X    7T 

The  resistance  which  a  coil  of  wire  of  known  resistivity  will 
offer  when  wound  on  a  given  bobbin,  is: 

rm  =  Lm  X  pm  ohms, (259) 

or,  by  inserting  the  value  of  Zm  from  (254) : 

rm  =  .262  X  An  X  (dm  +  //m)  X  l-~~~  •     (260) 

The  diameter  of  a  wire  which  shall  fill  a  bobbin  of  given 
dimensions  and  offer  a  given  resistance  can  be  found  as  fol- 
lows: The  coil  space  occupied  by  Zm  feet  of  wire  having  a 
diameter  (insulated)  of  S'm  inch,  is: 

Fm  =  12  Zm  X  <?'m2,     (261) 

while,  expressed  in  the  dimensions  of  the  bobbin,  the  same 
volume  is: 


362  DYNAMO-ELECTRIC  MACHINES.  [§95 

consequently  we  have: 


=  .262  x-x  (A.4.  +  V).     .-.(263) 

-^m 

In  order  to  replace  in  this  formula  the  unknown  length  Lm  , 
by  the  given  resistance,  rm,  we  express  the  latter  by  the 
dimensions  of  the  wire.  The  resistance  of  a  copper  rod  of  one 
square  inch  area  and  one  inch  length  being  .000000675  ohm  at 
15.  5°-  Cent.  (=  60°  Fahr.  ),  that  of  a  copper  wire  of  length 
Zm  feet  and  diameter  dm  inch,  is: 

rm  =  .000000675  x    I2Z™    ........  (264) 


Inserting  the  value  of  Zm  from  (264)  into  (263),  we  have: 
.000000675  X   12  X  /m  X  — 


x  <yma  x  - 

4 


=  .0000027  X  -       m  .  ,  X(tm  d 


m 


whence: 


X  *'.  =.  0000027  X         X  (*_  4.  +  V) 

-x(^m<41  +  V)  ..........  (265) 


In  practical  cases  the  diameters  dm  and  6'm  are  usually  very 
little  different  from  each  other,  so  that  with  sufficient  accuracy 
we  can  put  6m  X  tf^  =  #m2,  and,  consequently,  from  (265): 


=          .00,64  X  _  x  (/,„,  <  +  V) 


=  •04  X        ~-(hmd^-h^)  ...........  (266) 


§96]  COIL    WINDING   CALCULATIONS.  363 

In  order  to  allow  for  the  difference  between  tfm  and  d'm,  for 
irregularities  in  the  winding,  and,  eventually,  for  insulation 
between  the  layers,  the  next  smaller  gauge  wire  should  be 
taken.  The  selection  of  the  next  smaller  size  of  wire  is  par- 
ticularly necessary  in  case  of  winding  an  existing  spool,  since 
a  length  of  this,  effecting  the  given  resistance,  will  not  quite 
fill  the  coil  space,  while  for  the  next  larger  size  of  wire  the 
spool  would  not  hold  enough  of  the  wire  to  produce  the 
required  resistance.  •  , 

96.  Size  of  Wire  Producing  Given  Magnetizing  Force 
at  Given  Yoltage  Between  Field  Terminals.  Cur- 
rent Density  in  Magnet  Wire. 

Designating  the  E.  M.  F.  between  the  terminals  of  the  mag- 
net winding  by  ^"m,  the  current  flowing  through  the  field  cir- 
cuit by  7m,  and  the  magnet  resistance  by  rm,  Ohm's  Law 
furnishes  the  relation: 


Multiplying  both  sides  of  this  equation  by  the  length  of  the 
wire,  Lm  ,  we  obtain  : 


(267) 


But,  the  total  length,  in  feet,  of  the  magnet  wire  is  the 
product  of  the  number  of  convolutions,  JV"m  ,  and  of  the  mean 
length  of  one  turn,  /t,  in  feet,  thus: 

An  =  ^m  x  /t  ; 
furthermore,  by  (259): 


hence, 

AT      y   /      y    /    — 
•^m    /N   -*  m  *   ~~     n      ' 

/  m 

from  which  follows  the  specific  length  of  the  wire  which  gives 
the  desired  magnetizing  force  at  the  specified  voltage  between 
the  field  terminals,  viz.  : 


m 


X  /m)  X  /t   ..    ATX  /t 

" 


364  DYNAMO-ELECTRIC  MACHINES.  [§96 

that  is  to  say,  the  specific  length  (feet  per  ohm)  of  the  required 
wire  is  the  quotient  of  the  number  of  ampere-feet  by  the  given 
voltage.  In  taking  from  the  gauge  table  the  standard  size  of 
wire  whose  feet  per  ohm  are  nearest  to  the  figure  found  by 
(268),  the  size  of  magnet  wire  that  furnishes  the  required  num- 
ber of  ampere-turns,  AT,  at  the  given  potential  difference^, 
can  directly  be  determined  by  the  length,  /t,  of  the  mean  turn. 

Since  the  value  of  —  ,  from  (268),   gives  the  specific  length  of 

the  hot  magnet  wire,  the  next  smaller  gauge  number  should  be 
chosen. 

Inserting  (259)  into  (267)  we  obtain: 

T      y    T       -  ^n.    or  —      -    Zm   X    ft* 

•*•  m  A  -^m  —'     _      >  "  ' 


which,  multiplied  by  the  sectional  area  of  the  wire,  tfm2 ,  gives 
the  cross-section  of  the  wire  per  unit  of  current  strength,  that 
is,  its  current  density: 

_  tfm2  _  Zm 

m  T     '   ~    771      ^^     \    in      ^^    /  m/  * 

m          "^^m 

The  product  (#m2  x  An)  °f  the  sectional  area  (in  circular 
mils)  of  a  wire  into  its  specific  resistance  (in  ohms  per  foot) 
gives  the  resistance  of  one  mil-foot  of  wire  of  the  given 
material,  i.  e.,  in  the  case  of  copper: 

#mJ  X  pm  —  12  ohms,  at  about  60°  Cent.  (—  140°  Fahr.); 
consequently  the  current  density  in  the  magnet  wire: 


(269) 


For  a  given  machine,  therefore,  (^"m  being  constant)  the  cur- 
rent density  only  depends  upon  the  total  length  of  the  wire, 
and  is  independent  of  its  size. 

Formula  (269)  may  be  used  to  determine  the  practical  limits 
of  Zm  ,  by  limiting  the  value  of  the  current  density,  /m.  From 
(269)  follows  directly: 

An=      -x^m;  .............  (270) 


g96]  COIL    WINDING  CALCULATIONS.  365 


and  since  the  practical  value  of  /m  ranges  between  240  and 
1800  Circular  Mils  per  ampere  (=  5300  to  700  amperes- per 
square  inch,  or  8. 2  to  i.i  amperes  per  square  millimetre), 
we  have: 


.M.  per  amp.   .  .(-£m)min  =    20^m;  )     /« 
for  (jm)ma*  =  i, 800  C.  M.  per  amp.   . .  (Lm)max  =  150  £m.  } 

The  total  length  of  magnet  wire,  in  feet,  should  therefore 
be  from  20  to  150  times  the  difference  of  potential  between  the 
field  terminals,  in  volts. 

From  (269)  we  can  also  derive  the  following  formula,  which 
gives,  directly  in  Circular  Mils,  the  area  of  a  magnet  wire 
effecting  a  certain  magnetizing  force  at  given  potential  between 
field  terminals,  viz.  : 

12     X    An     X    /m  12    X    Nm    X    /m    X   /t 


(Nm  X  /...)  X  (it  X  /t)  _ATxft 


that  is  to  say,  the  area  of  the  requisite  magnet  wire  is  the 
quotient  of  the  number  of  ampere-inches  (/T  being  the  length 
of  the  mean  turn  in  inches)  to  be  wound  upon  the  cores,  by 
the  potential  between  the  field  terminals.  Assuming  an  ap- 
proximate value  for  the  mean  turn,  /T ,  the  minimal  limit  of 
which  is  always  given*  by  the  circumference  of  the  magnet 
core,  a  preliminary  value  of  dm  can  be  quickly  determined,  and 
from  this  the  value  of /T  is  easily  adjusted  if  necessary;  a  re- 
calculation with  the  correct  value  of  /T  will  then  furnish  the 
final  value  of  the  area  of  the  magnet  wire. 

A  set  of  valuable  curves  which  show  the  relation  between 
ampere-turns  and  mean  length  of  turn,  and  between  current 
and  total  length  of  wire,  respectively,  and  which  can  be  used 
for  graphically  obtaining  the  results  of  formula  (272)  as  well 
as  other  data  concerning  the  magnet  winding,  has  been 
devised  by  Harrison  H.  Wood.1 

Formula  (272)  is  only  approximate,  being  based  upon  the 
assumption  that  the  final  temperature  of  the  magnet  coils  is 


1  "Curves  for  Winding  Magnets,"  by  H.  H.  Wood;  Electrical   World,   vol. 
xxv.  pp.  503  and  529  (April  27  and  May  4,  1895). 


366  DYNAMO-ELECTRIC  MACHINES.  [§96 

about  60°  C.  If  the  actual  rise  above  15.5°  C.  of  the  magnet 
temperature  is  denoted  by  6m,  the  accurate  formula  for  the 
area  of  the  wire  would  be  : 


10.5  being  the  resistance,  in  ohms,  of  a  copper  wire,  one  foot 
long  and  one  mil  in  diameter,  at  a  temperature  of  15.5°  C. 
(=  60°  F.). 

From  (273)  a  very  useful  formula  for  the  weight  of  the  mag- 
net winding  can  be  derived.     By  Ohm's  Law  we  have: 

p 

-^m   —   •*  m    X    T'm   ~:   ~J?~    X    ^m  ) 
^m 

in  which  Pm  =  energy  absorbed  in  magnet  winding,  in  watts 
(see  §  98);  consequently: 


But  the   resistance   of   the   magnet    winding    can    be   ex- 
pressed by: 


x  (I  +  -004  x  ^  x    "  x 


where  wt'm  =  weight  of  magnet  winding,  including  insulation, 

in  pounds; 

klb  =  specific  weight  of  magnet  winding,  in  pounds 
per  cubic  inch,  depending  upon  size  of  wire 
and  thickness  of  insulation;  see  Table  XCII. 

Hence: 

,  12  X  io-6  X  k»  X  AT  X  /t  X  £m  X  #m4 

Pm  X  wt'm 
or, 

_  12  X  io~6  X  /£1B  X  AT  X  /t  X^gm  X  ^ma 

^  '  m   —  TJ  > 

-*  m 

and  since  by  (272)  we  have,  approximately: 

&m    X    <^m2    =    12    X    4T   X    /tl. 


§96]  COIL    WINDING   CALCULATIONS. 

we  finally  obtain: 

wfm  =  144  X  io~6X  klt  X 
or, 


367 


/^rx  4V 
I    1000    y 


(374) 


The  constant  /&16  is  =  144  X  £16,  and  can  be  taken  from  the 
following  Table  XCII. : 

TABLE    XCII. — SPECIFIC  WEIGHTS  OF    COPPER  WIRE   COILS,    SINGLE 
COTTON  INSULATION. 


Total 

Area 

Specific 

Value 

GAUGE 
OP  WIRE. 

Diam- 
eter, 
Bare, 
Inch. 

Insula- 
tion 
S.  C.  C. 
Inch. 

Space 
Occupied 
by  Wire. 
Cir.  Mils. 

of 
Copper. 
Square 
Mils. 

Ratio 
of 
Copper 
to 

Weight 
of 
Winding. 
Ibs.  per 

of 
Constant 
in 
Formula 

Total 

cu.  inch. 

(274). 

Volume 

of 

t 

7T 

Coil. 

B.  W.  G. 

B.  &S. 

m 

6m~6m 

m 

1 

&15 

&li 

re) 

4 

.204 

.012 

46,656 

32,685 

.702 

.225 

32.5 

(7) 

5 

.182 

.012 

37,637 

26,016 

.69 

.221 

31.8 

8 

.165 

.012 

31,329 

21,383 

.683 

.218 

31.4 

'e 

.162 

.010 

29,584 

20,612 

.697 

.223 

32.2 

*9 

.148 

.010 

24,964 

17,203 

.688 

.220 

31.7 

10 

(8) 

.134 

.010 

20,736 

14,103 

.682 

.218 

31.4 

11 

(9) 

.120 

.010 

16,900 

11,310 

.669 

.214 

30.8 

12 

.109 

.010 

14,161 

9,331 

.66 

.211 

30.4 

io 

.102 

.010  ' 

12,544 

8,171 

.65 

.208 

30.0 

is 

.095 

.010 

11,025 

7,088 

.644 

.206 

29.7 

ii 

.091 

.010 

10,209 

6,504 

.637 

.204 

29.4 

(14) 

12 

.081 

.007 

7,744 

5,153 

.665 

.213 

30.7 

15 

13 

.072 

.007 

6,241 

4,072 

.65 

.208 

30.4 

16 

(14) 

.065 

.007 

5,184 

3,318 

.64 

.205 

29.5 

17 

(15) 

.058 

.007 

4,225 

2,642 

.625 

.200 

28.8 

(18) 

16 

.051 

.007 

3,364 

2,043 

.607 

.194 

27.9 

17 

.045 

.005 

2,500 

1,590 

.637 

.204 

29.5 

19 

.042 

.005 

2,209 

1,385 

.627 

.201 

29.0 

18 

.040 

.005 

2.025 

1,257 

.628 

.201 

29.0 

19 

.036 

.005 

1,681 

1,018 

.607 

.194 

27.9 

20 

.035 

.005 

1,600 

962 

.601 

.1925 

27.7 

21 

20 

.032 

.005 

1369 

804 

.587 

.187 

27.0 

22 

21 

.028 

.005 

1,089 

616 

.546 

.175 

25.2 

23 

22 

.025 

.005 

900 

491 

.565 

.181 

26.1 

24 

23 

.022 

.005 

729 

380 

.521 

.167 

24.1 

25 

24 

.020 

.005 

625 

314 

.503 

.161 

23.2 

26 

25 

.018 

.005 

529 

254.5 

.48 

.1535 

22.1 

27 

26 

.016 

.005 

441 

201 

.457 

.146 

21.0 

28 

27 

.014 

.005 

361 

154 

.428 

.137 

19.8 

29 

28 

.013 

.005 

324 

133 

.41 

.131 

18.9 

30 

.012 

.005 

289 

113 

.391 

.125 

18.0 

29 

.011 

.005 

256 

95 

.371 

.119 

17.2 

From  the  above  Table  it  is  found  that  for  the  most  usual 
sizes  of  magnet  wire  (No.  6  B.  W.  G.  to  No.  20  B.  W.   G.)  the 


DYNAMO-ELECTRIC  MACHINES.  [§97 

average  value  of  klt  is  =  .21,  and  that  of  klt  is  =  30,  and 
therefore  approximately: 


(AT  X  /A2 
3o  x  (  -      -^—  '  J 
y    1000      / 


(275) 

m 
that  is  to  say  : 

x  /Ampere-feety 

I  1000  ) 

Weight  of  winding  =  Watts  absorbed  by^Magnet  Winding.  ' 

By  means  of  (275)  the  weight  of  wire  can  be  found  that  sup- 
plies a  given  magnetizing  force  at  a  fixed  loss  of  energy  in  the 
field  winding. 

97.  Heating  of  Magnet  Coils. 

The  conditions  of  heat  radiation  from  an  electro-magnet 
being  similar  to  those  of  an  armature  at  rest,  with  polepieces 
removed,  the  unit  temperature  increase  of  magnet  coils  can  be 
obtained  by  extending  Table  XXXVI.,  §  35,  for  the  specific 
increase  of  armatures,  to  conform  with  the  above  conditions. 
Plotting  for  this  purpose  the  temperatures  given  in  the  first 
horizontal  row  for  zero  peripheral  velocity,  as  functions  of  the 
ratio  of  pole-area  to  total  radiating  surface,  and  prolonging 
the  temperature  curve  so  obtained  until  it  intersects  the  zero 
ordinate,  the  specific  temperature  rise  0'm  —  75°  C.(=  135°  F.) 
for  i  watt  of  energy  loss  per  square  inch  of  radiating  sur- 
face, is  found.  The  actual  temperature  increase  of  any  mag- 
net coil  can,  therefore,  be  obtained  by  the  formula: 

P 


v  y  HI 

"m   —   "m    *      £—  —     /  5       X    -£-  ,         

where  0m    =  rise   of  temperature   in   magnets,    in  Centigrade 

degrees; 
Pm  =  energy  absorbed  in  magnet-winding,  in  watts; 

(  Im  =  current  in  magnet  wind- 
ing, in  amperes; 
JSm  -  E.    M.   F.    between  field 

terminals,  in  volts; 
rm    =  resistance     of      magnet 

winding,  in  ohms; 
=  radiating  surface  of  magnet  coils,  in  square  inches. 


§  97]  COIL    WINDING  CALCULA  TIONS.  369 

The  radiating  surface  of  the  magnets  depends  upon  the  shape 
and  size  of  the  cores  as  well  as  the  upon  the  arrangement  of  the 
field  frame,  and  can  be  readily  deduced  geometrically  from 
the  dimensions  of  the  coil.  If  the  polepieces,  or  yokes,  com- 
pletely overlap  the  end  flanges  of  the  magnet  coils,  air  has 
access  to  the  prismatical  surface  only,  and  the  radiating  sur- 
face is — 
for  cylindrical  magnets: 

SM   =   An    X    71    X    /'m   =    (4n  +   2/fcm)    X    7t    X    /'m  J       (277) 

for  rectangular  magnets: 

SM  =  2  X  /'m  X   (/  +  ^-Mm  X  *);      ....(278) 

and  for  magnets  of  oval  cross-section  (rectangle  between  two 
semicircles) : 


-  2  X  /'m  X 


[('  -  *)  +  (2~  +  *-  )  X  *]  •    --(279) 


In  case  that  also  one  of  the  end  surfaces  of  each  coil  is 
exposed  to  the  air,  or  that  one-half  of  each  coil  flange  helps 
the  prismatical  surface  to  liberate  the  heat  developed  by  the 
field  current,  the  radiating  surface  becomes: 

•SM,  =  SM  +  *m  X  /T  X  /*m (280) 

If  there  is  ,a  clearance  between  the  magnet  coils  and  the 
yokes  and  polepieces  such  as  to  make  both  the  entire  end  sur- 
faces of  each  magnet  coil  active  in  giving  off  heat,  the  radiat- 
ing surface  is: 

^M2    =    ^M   +   2«m    X    /T    X    ^m (281) 

And  when,  finally,  the  yokes  and  polepieces  touch  the  end 
flanges  of  the 'coils,  but  the  latter  project  over  the  former  so 
that  heat  can  radiate  from  the  projecting  portions,  the  radiat- 
ing surface  will  be: 

^M3  =  SM  +  2«m  x  hm  x  (/T  -  *y) (282) 

In  the  above  formula  (277)  to  (282): 

SM  =  radiating  surface  of  prismatic  surface  of  magnet 

coil; 
•SMI  —  radiating  surface  of  prismatic  surface  plus  one 

end  surface  per  coil; 


37°  DYNAMO-ELECTRIC  MACHINES.  [§97 

•S*M2  =  radiating  surface  of  prismatic  surface  plus  two 
end  flanges  per  coil; 

SMS  =  radiating  surface  of  prismatic  surface  plus  pro- 
jecting portions  of  coil  flanges; 

dm    =  diameter  of  circular  core-section; 

Z>m  =  external  diameter  of  cylindrical  magnet  coil; 

hm  =  height  of  magnet  winding,  see  Table  LXXX., 
§83; 

l'm  =  total  length  of  magnet  coils  per  magnetic 
circuit; 

/      —  length  of  rectangular  or  oval  core-section; 

b      =  breadth  of  rectangular  or  oval  core-section; 

/T     —  length  of  mean  turn  of  magnet  wire; 

by     =  breadth  of  yoke,  or  polepiece; 

nm  =  number  of  separate  magnet  coils  in  each  mag- 
netic circuit. 

If  the  surface,  ^'M,  of  the  magnet  cores  is  given  instead  of 
the  radiating  surface,  SM,  of  the  coils,  the  value  of  fl'm  in  (276), 
instead  of  being  constant  at  75°  C.,  ranges  between  75°  and 
4°  C.  (or  135°  and  7°  F.,  respectively),  according  to  the  ratio 
of  depth  of  magnet  winding  to  thickness  of  core;  that  is, 
according  to  the  ratio  of  radiating  surface  to  core  surface.  In 
the  following,  Table  XCIIL,  the  specific  temperature  rise,  0'm, 
is  given  for  round  magnets,  varying  in  winding  depth  from  .01 
to  2  core  diameters,  and  for  rectangular  and  oval  cores  ranging 
in  radiating  surface  from  1.02  to  15  times  the  surface  of  the 
cores. 

If,  for  a  given  type  of  machine,  the  approximate  ratio  of 
radiating  surface  to  core  surface  is  known,  the  calculation  of 
the  magnet  winding  can,  by  means  of  Table  XCIIL,  directly 
be  based  upon  the  given  surface  of  the  magnet  cores. 


98.    Allowable  Energy   Dissipation  for  Giyen  Rise  of 
Temperature  in  Magnet  Winding. 

From  formula  (276),  §  97,  it  is  evident  that  for  a  given  coil 
the  temperature  rise  depends  solely  upon  the  amount  of  energy 
consumed,  and  conversely  it  follows  that  by  limiting  the  tern- 


97] 


COIL    WINDING   CALCULATIONS. 


371 


Il 

fc  P 

O  02 

a 


p 


goj 
32 


Is  II 


e  of 
per 


||   .o 


!!•§?  1 


a^ 

!I 


iK^ 


£».; 


o     c. 

S^l« 


i.l  O  O  »O 


O  O 


mo      10      o 


*  000*00 


•^t-OOOifSOOOOQOQ 

o  q  T-I  i-,  o<  <N  co  oo  n;  •*  55  «q  35     iq 

^r^^r^^^^rt^T^TH^r-fOJfNTttSOQO 


8OOOOQOOOOOO 
i-H  i-<  «  (N  «  TC_  r).  O  O  «5  I>       O       00 
^  ^  ^'  r4  TH'  rH  r^  I-!  rH  r^  r4  T-H  5<  Ot  CO  O  00  <N 


^  ^  ^ ,_;  rt'  oi  eo  o  «o 


^W 

O  O 


rH  r-(  r-5  rt  JH  <N  S{  CO  >O       MS 


372  DYNAMO-ELECTRIC  MACHINES.  [§98 

perature  increase  of  the  coil,  the  maximum  of  its  energy  dissi- 
pation is  also  fixed.     By  transposition  of  (276)  we  obtain: 

Jpm  =  ^oX5M,     (283) 

and 

;    (284) 


where  Pm  =  energy  dissipation  in  magnet  winding,  in  watts; 
0m    =  temperature  increase  of  magnet  coils,  in  degrees 

Centigrade; 
6'm   =  specific   temperature   rise   of   magnet   coils,  per 

watt  to  the  square  of  core  surface; 
SM    =  radiating    surface    of    magnet  coils,    in    square 

inches;  see  formulae  (277)  to  (282); 
6"M   =  surface  of  magnet  cores,  in  square  inches. 

The  temperature  rise  of  magnet  coils  in  practice  varies  be- 
tween 10°  and  50°  C.,  and  in  exceptional  cases  reaches  75°  C., 
'the  latter  increase  causing,  in  summer,  a  final  temperature  of 
the  magnets  of  about  100°  C.,  which  is  the  limit  of  safe  heating 
of  coils  of  insulated  wire.  For  ordinary  cases,  therefore,  the 
allowable  energy  dissipation  in  the  field  magnets  ranges 
between 

P  —  v    S1 

75 

and 

^m  =    p  X  SM  =  .667^, 

that  is,  between  .133  and  .667  watt  per  square  inch  (=  .02  to 
.10  watt  per  square  centimetre),  or  radiating  surface  is  to  be 
provided  at  the  rate  of  from  7^  to  i^  square  inches  per 
watt  (=  50  to  10  square  centimetres  per  watt).  The  arith- 
metical mean  of  these  limits,  .4  watt  per  square  inch  (=  .062 
watt  per  square  centimetre),  or  2%  square  inches  (=  16 
square  centimetres)  per  watt,  is  a  good  practical  average  for 
medium. sized  machines,  and  corresponds  to  a  rise  of  magnet 
temperature  of  30°  C.  (=  54°  F.). 

The  energy  dissipation,  Pmi  thus  being  fixed  by  the  temper- 


§  98]  COIL    WINDING  CALCULA  TIONS.  373 

ature  increase  specified,  the  working  resistance  of  the  magnet 
winding  can  be  obtained  by  means  of  Ohm's  Law,  thus^ 


F  F     v    /  P 

r'm  =  -f  =     -/;   m  =  %$ (285) 

ym  Jm  Jm 


or, 


according  to  whether  the  intensity  of  the  current  flowing 
through  the  field  circuit,  or  the  E.  M.  F.  between  the  field  ter- 
minals, respectively,  is  given,  the  former  being  the  case  in 
series-wound  machines  and  the  latter  in  shunt-wound  dynamos. 
In  a  series  machine  the  field  current  is  equal  to  the  given  cur- 
rent output,  7m  =  /;  while  in  a  shunt  dynamo  the  potential 
between  the  field  terminals  is  identical  with  the  known  E.  M. 
F.  output  of  the  machine,  £m  =  E\  see  §  14,  Chapter  II. 


CHAPTER  XX. 

SERIES    WINDING. 

99,  Calculation  of  Series  Winding  for  Given  Tempera- 
ture Increase. 

The  number  of  ampere-turns,  AT,  being  found  by  the  for- 
mulae given  in  Chapter  XVIII.  ,  and  the  field  current  in  a  series 
dynamo  being  equal  to  the  given  current  output,  /,  of  the 
machine,  the  number  of  series  turns,  Nae,  can  readily  be 
obtained  by  dividing  the  former  by  the  latter: 

A  f 

#.=   -r  ...............  (287) 

The  number  of  turns  multiplied  by  the  mean  length  of  one 
convolution,  in  feet,  gives  the  total  length  of  the  series  field 
wire: 


(288) 


in  which  the  length  of  the  mean  turn,  in  inches,  is  — 
for  cylindrical  magnets  : 

4  =   (4n  +  /V)    X    7t',    ...........  (289) 

for  rectangular  magnets  : 

/T  =  2  X  (/  +  V)  +  hm  X  7t  ;    .......  (290) 

and  for  oval  magnets  (rectangle  between  two  semicircles)  : 

/T  =  2   X   (/  -  b)  +  (b  +  /im)  X  7t  ;    .  .  .  .(291) 

where  dm  =  diameter  of  circular  core-section; 

/     =  length  of  rectangular  or  oval  section; 

b     =  breadth  of  rectangular  or  oval  section; 

hm  =  height  of  magnet  winding,  from  Table  LXXX., 


374 


99] 


SERIES    WINDING. 


375 


An  approximate  value  for  the  length  of  the  average  turn  for 
cylindrical  magnets  can  be  obtained  from 

/,=  *„  x  dm,   (292) 

where  £17  =  ratio  of  length   of  mean  turn  to  core   diameter, 
see  Table  XCIV. 

The  ratio  £17  depends  upon  the  size  of  the  magnet,   and 
ranges  as  follows: 

TABLE  XCIV.— LENGTH  OF  MEAN  TURN  FOR  CYLINDRICAL 
MAGNETS. 


DIAMETER 

HEIGHT 
OF  WINDING  SPACE, 

RATIO 
or  MEAN  TURN 
TO  CORE  DIAMETER, 

OF 

MAGNET 

hm 

(4n  +  ^»)    X    7T 

CORE, 
^m 

INCHES. 

7    ~                   4n 

INCHES. 

Bipolar 
Types. 

Multipolar 
Types. 

Bipolar 
Types. 

Multipolar 
Types. 

1 

i 

I 

4.71 

5.50 

2 

i 

u 

4.32 

5.11 

3 

1 

11 

4.19 

4.97 

4 

U 

2 

4.12 

4.71 

6 

H 

a* 

3.93 

4.32 

8 

If 

a* 

3.83 

4.12 

10 

1* 

8* 

3.73 

4.01 

12 

2 

3 

3.66 

3.93 

15 

2i 

8i 

3.59 

3.82 

18 

2i 

w 

3.54 

3.75 

21 

»f 

to 

3.50 

3.70 

24 

2* 

4 

3.47 

3.67 

27 

at 

4± 

3.45 

3.64 

30 

2£ 

41 

3.43 

3.62 

33 

a| 

4f 

341 

3.60 

36 

3 

5 

3.40 

3.58 

The  averages  given  for  the  height  of  the  winding  space  /*m, 
in  Tables  LXXX.  and  XCIV.,  enable  an  approximate  value  of 
the  radiating  surface,  »$*„,  to  be  found  by  formulae  (277)  to 
(282),  respectively,  and  the  latter,  together  with  the  specified 
temperature  increase,  0m,  furnishes  the  allowable  energy  dis- 
sipation, P^  ,  by  virtue  of  equation  (283).  From  formula 
(285),  then,  the  required  series  field  resistance  can  be  obtained 
thus: 


'»  =         -  rr  X       , 

yse  75  2 


15.5 


(293) 


37*  DYNAMO-ELECTRIC  MACHINES.  <§  99 

or: 

*.5.5°C.     ..(294) 


In  dividing  (288)  by  (294),  finally,  the  specific  length  Ase,  in 
feet  per  ohm,  of  the  series  winding  giving  a  magnetizing  force 
of  AT  ampere-turns  at  a  rise  of  the  magnet  temperature 
of  0m  degrees  Centigrade,  is  received,  viz. : 

AT      _4_ 
A     -  ^-5  -  T~  <  J7_ 

7s  X  /2   Ki-f-.oo4  X  0m 
^  T  v  /    v   / 

=  6.25  x  -    8  V  *  - x  (l  +  -°°4  x  •„,) ,     ... .(295) 


m 


where  A  T  —  ampere-turns  required  for  field  excitation,   for- 

mula. (227); 
/T    =  length  of  mean  turn,  in  inches,  formulae  (289)  to 

(292),  respectively; 

/    =  current  output  of  dynamo,  in  amperes; 
9m  =  specified  temperature  increase  of  magnet  wind- 

ing, in  Centigrade  degrees; 
SK  =  radiating   surface    of   magnet   coils,     in    square 

inches,  formulae  (277)  to  (282). 

The  conclusion  of  the  series  field  calculation,  now,  consists 
in  selecting,  from  the  standard  wire  gauge  tables,  a  wire 
whose  "  feet  per  ohm  "  most  nearly  correspond  to  the  result 
of  formula  (295).  If  no  one  single  wire  will  satisfactorily 
answer,  either  n  wires  of  a  specific  length  of 

A. 

n 

feet  per  ohm  each  may  be  suitable  stranded  into  a  cable,  or  a 
copper  ribbon  may  be  employed  for  winding  the  series  coil. 
In  the  latter  case  it  is  desirable  to  have  an  expression  for  the 
sectional  area  of  the  series  field  conductor.  Such  an  expres- 
sion is  easily  obtained  by  multiplying  the  specific  length,  Ase  , 
by  the  specific  resistance,  for,  since 

.-  feet 

ohms  =  specific  resistance  X  -»  -  =  -  n-» 

circular  mils 


§  100]  SERIES    WINDING.  377 

we  have: 

circular  mils  =  specific  resistance  X  feet  per  ohm; 

the  specific  resistance  of  copper  is  10.5  ohms  per  mil-foot,  at 
15.5°  C.,and  the  area  of  the  series  field  conductor,  conse- 
quently, is: 

tfse2  =  10.5  X  Ase 


=  65  X        Xv%x/x(i+.oo4xem).    ...(296) 

m   A    OM 

In  formulae  (293)  to  (296),  it  is  supposed  that  all  the  mag- 
net coils  of  the  machine  are  connected  in  series.  If  this, 
however,  is  not  the  case,  the  main  current  must  be  divided  by 
the  number  of  parallel  series-circuits,  in  order  to  obtain  the 
proper  value  of'/  for  these  formulae. 

Having  found  the  size  of  the  conductor,  the  number  of 
turns,  NKy  from  (287),  will  render  the  effective  height,  A'm, 
of  the  winding  space  for  given  total  length,  /'m,  of  coil,  by 
transposition  of  formula  (252),  §  95,  thus: 

#-*.#»  x  ^^,  ...........  (297) 

^  m 

(tf'se)2  being  the  area,  in  square  inches,  of  the  square,  or  rectan- 
gle, that  contains  one  insulated  series  field  conductor  (wire, 
cable,  or  ribbon). 

If  h'm,  from  (297),  should  prove  materially  different  from  the 
average  winding  depth  taken  from  Table  LXXX.,  the  actual 
values  of  /T  and  SM  should  be  calculated,  and  the  size  of  the 
series  field  conductor  checked  by  inserting  these  actual  values 
into  formula  (295)  or  (296). 

The  product  of  the  number  of  turns  by  the  actual  mean 
length  of  one  convolution  will  give  the  actual  length,  Zse  ,  of 
the  series  field  winding,  and  from  the  latter  the  real  resistance 
and  the  weight  of  the  winding  can  be  calculated.  (See  §  102.) 

100.  Series  Winding  with  Shunt  Coil  Regulation. 

For  some  purposes  it  is  desired  to  employ  a  series  dynamo 
whose  voltage  can  be  readily  adjusted  between  given  limits. 
Such  adjustment  can  best  be  attained  by  connecting  across 
the  terminals  of  the  series  field  winding  a  shunt  of  variable 


378 


DYNAMO-ELECTRIC  MACHINES. 


[§100 


resistance  which  is  opened  if  the  maximum  voltage  is  desired, 
while  its  least  resistance  is  offered  for  obtaining  the  minimum 
voltage  of  the  machine,  intermediate  grades  of  resistance  being 
used  for  regulating  the  voltage  of  the  machine  between  the 
maximum  and  the  minimum  limits.  The  series  winding  in 
this  case  is  calculated,  according  to  §  99,  for  the  maximum 
voltage  of  the  machine,  and  then  the  various  combinations  of 
the  shunt-coils  are  so  figured  as  to  produce  the  desired  regu- 
lation, and  to  safely  carry  the  proper  amount  of  current. 

As  an  example  let  us  take  five  coils  arranged,  as  shown  in 
Fig.  305,  so  as  to  permit  of  being  grouped,  by  moving  the 


SERIES  FIELD  WINDING 


FIG.  305 
DIAGRAM  OF  SERIES  WINDING 

WITH  SHUNT  COIL  REGULATION. 


FIG.  309 
4TH  COMBINATION 


FIG.  310 

5TH  COMBINATION. 


Figs.  305  to  310. — Shunt  Coil  Combinations. 

slider  of  the  adjusting  switch  into  five  different  combinations, 
illustrated  by  Figs.  306  to  310. 

The  resistances  and  sectional  areas  of  these  coils  are  to  be 
so  determined  as  to  enable  60,  66f,  75,  83^-,  and  90  per  cent, 
of  the  maximum  voltage  to  be  taken  from  the  machine.  It  is 
evident  that  in  this  case  40,  33^-,  25,  i6f,  and  10  per  cent,  re- 
spectively, of  the  maximum  field  current  will  have  to  be 
absorbed  by  the  respective  combinations  of  the  shunt  coils, 
and  their  resistance,  therefore,  must  be: 

Resistance  first  combination 

-  X  resistance  of  series  field  =1.5  /se. 
40 

Resistance  second  combination 


X  resistance  of  series  field  =  2 


33i 


§  1OO]  SERIES    WINDING.  379 

Resistance  third  combination 

7  ^ 

X  resistance  of  series  field  =  3  r'8e . 
Resistance  fourth  combination 


=  ~~M  x  resistance  of  series  field  —  5  r'K . 
Resistance  fifth  combination 

X  resistance  of  series  field  =  9  r'8e . 

For  the  arrangement  shown  in  Figs.  305  to  310,  the  first 
combination  consists  of  coils  I,  II,  and  III,  in  parallel,  the 
second  combination  of  coils  II  and  III  in  parallel,  in  the  third 
combination  only  coil  III  is  in  circuit,  in  the  fourth  combina- 
tion coils  III  and  IV  are  in  series,  and  the  fifth  combination 
has  coils  III,  IV,  and  V  in  series.  In  all  combinations  there 
are,  furthermore,  the  flexible  leads  carrying  the  current  from 
the  field  terminal  to  the  adjusting  slider;  these  are  in  series 
to  the  group  of  coils  in  every  case,  and  their  resistance,  rt , 
consequently  is  to  be  deducted  from  the  resistance  of  the 
combination  in  order  to  obtain  the  resistance  of  the  group  of 
coils  alone.  Expressing  the  resistances  of  the  various  groups 
by  the  resistances  of  the  single  shunt-coils,  we  therefore  obtain : 

First  group: 

^  -7--  i-s^-n;    (298) 

'i  rn          rm 

Second  group: 

r  =  *'--*;     (299) 

~ ^   ^~ 

Third  group: 

rm  =  3r'se  -  ri;     (300) 

Fourth  group : 

'm  +  *w  =  s^'se-  n;    (301) 

Fifth  group: 

>m  +  '„  +  rv  =  g  r'se  -  r, (302) 

From  this  set  of  equations  the  resistances  of  the  separate 
shunt-coils  can  be  derived  as  follows: 


0  DYNAMO-ELECTRIC  MACHINES.  [§  1OO 

Inserting  (299)  into  (298) : 


ri         2  r  se  —  /-, 
whence: 

rj  =  (^  ^se  -  n)  X  (1.5  r'»  -  r,) 

=  3  r'se8    -   3-5   ^se^l  +   n2  _   6  r,  r      ,      2  fj* 

•S'-'se  '     r'se    ' 

The   resistance  of  the  leads  being  very   small,  r?  can  be 
neglected,  hence  the  resistance  of  coil  I: 

^•=6^-  7r, (303) 

(300)  into  (299)  gives: 
i 

"^+3  '.  -  ' 


or: 


-  (3  r'w  -  r,)  X  (2  r^  -  rQ 
(3  ^'se  -  n)  -  (  2  /se  -  r,) 


- 


Neglecting  again  r? ,  the  resistance  of  coil  II  is  obtained  : 

^n  =  6r'8e  -5^ (304) 

From  (300)  we  have,  directly: 

rm  =  3^'se-  n (305) 

By  subtracting  (300)  from  (301): 

rjf;±=  2/se (306) 

By  subtracting  (301)  from  (302): 

rv  =  4r'se. (307) 

In  the  above  formulae,  r'^  is  the  resistance  of  the  series 
field,  hot,  at  maximum  E.  M.  F.  output  of  machine;  and  rt  the 
resistance  of  the  current-leads  at  the  temperature  of  the 


§  100]  SERIES    WINDING.  381 

room.  The  resistance  r\  is  determined  by  finding  the  length 
and  the  sectional  area  of  the  leads,  the  former  being  depend- 
ent upon  the  distance  of  the  adjusting  switch  from  the  field 
terminal,  and  the  latter  upon  the  maximum  current  to  be  car- 
ried, which  in  the  present  case  is  40  per  cent,  of  the  current 
•output  of  the  machine. 

The  currents  flowing  through  the  shunt  coils  in  the  various 
combinations  can  be  obtained  by  the  well-known  law  of  the 
divided  circuit,  by  virtue  of  which  the  relative  strengths  of  the 
currents  in  the  different  branches  are  directly  proportional 
to  their  conductances,  or  in  inverse  proportion  to  their 
resistances. 

The  first  combination  consists  in  three  parallel  branches 
having  the  resistances  rl%  rn,  and  rm,  respectively,  and  carries 
a  total  current  of  .4  /  amperes,  hence  the  currents  in  the 
branches: 

rm  v     .    T 

—  :  —  «  -    x  .4  A 


m 


7n  =  —  -   X  .4 

ru  rm  +  ri  rm  T  ri  rll 


X    47. 


m 


Inserting  into  these  equations  the  values  of  the  resistances 
from  (303)  to  (307),  respectively,  we  obtain: 


y    __  (6r'se  — 

(6r'se  -  Sn)  dr'&e  -  r\)  +  (6r'se  -  7r\)  (zr'ee  -  r\)  +  (dr/se  -  ^)  (6r'se  - 


X.4/ 


y     ,/~Iv      i  7-       r/ 

>  4  X  -4 

iSr'^  -  28r'se  r,  +  7^  _  I 

7"  -  72^  -  i2i/86  r,  +         2  X  -4  7  -      X  .4  7  --  .1  7, 


and 

/       -  36r/M'  ~  72/8e  ri  +  35na    v     ,  T       T  v     ,  T         >  7 
-'m  —  -  r~a  --  /  -  f       —  a  X  -4-«   —  —  X  .4-«   z=:  .27. 
72r'se3  --  121^^  +  47^  2 

In    the    second    combination    there    are    but    two    parallel 


382  DYNAMO-ELECTRIC  MACHINES.  [§  10O 

branches,  having  the  resistances  ru  and  rm,  and  the  total  cur- 
rent carried  is  .333  /amperes  ;  therefore: 

/„   =  -^-  X  .333/=Q3;''eVr  X  '333  7 

^11  ~T  rIII  9r  se  ~~  °  r\ 

—  -  X  .333  7  =  -111  7> 
«5 

and 

^TT  6r'     —  <ri 

7m  =  r    +  r      X  .333  /  =  -r^-  -f-  !  X  -333  ' 
>H  T  rm  9^se  -'  0*1 

=  7   X  .333  /=  -222  7- 
3 

The  third,  fourth,  and  fifth  combinations  are  simple  circuits 
only,  the  current  through  the  coils  therefore  is  identical  with 
the  total  current  flowing  through  the  combination,  viz.  :  .25  /, 
.167  /and  .1  /amperes  respectively;  the  first  named  current, 
consequently,  flows  through  coil  III  when  in  the  third  com- 
bination, the  second  current  through  coils  III  and  IV,  when 
in  the  fourth  combination,  and  the  last  figure  given  is  the  cur- 
rent intensity  in  coils  III,  IV,  and  V,  when  in  the  fifth  com- 
bination. Taking  the  maximum  value  for  the  current  flowing 
in  each  coil,  the  following  must  be  their  current  capacities: 

Coil  I  and  V:   /,  =  7V  =  .1  /  =  —  ,     .........  (308) 

"    II:  /„  =  .in  /==-,     ........  (309) 

"  HI:  /m=.*5/=,     .......  (310) 


"   IV:  /IV  =  .i67/=,     ........  (311) 

By  allowing  1000  circular  mils  per  ampere  current  intensity, 
the  proper  size  of  wire  for  the  different  shunt  coils  can  then 
readily  be  determined  from  formulae  (308)  to  (311). 

The  preceding  formulae  (298)  to  (311)  of  course  only  apply 
to  the  special  arrangement  and  to  the  particular  regulation 
selected  as  an  example,  but  can  easily  be  modified  for  any 
given  case  [see  formulae  (457)  to  (466),  §  134],  the  method  of 
their  derivation  being  thoroughly  explained. 


CHAPTER   XXI. 

SHUNT    WINDING. 

101.  Calculation  of  Shunt  Winding   for  Giyen  Tem- 
perature Increase. 

The  problem  here  to  be  considered  is  to  find  the  data  for 
a  shunt  winding  which  will  furnish  the  requisite  magnetizing 
force  at  the  specified  rise  of  the  magnet  temperature,  and 
with  a  given  regulating  resistance  in  series  to  the  shunt  coils, 
at  normal  output. 

The  shunt  regulating  resistance,  or  as  it  is  sometimes  called, 
the  extra-resistance,  admits  of  an  adjustment  of  the  resistance 
of  the  shunt-circuit  within  the  limits  prescribed,  thereby 
inversely  varying  the  strength  of  the  shunt-current,  which  in 
turn  correspondingly  influences  the  magnetizing  force  and, 
ultimately,  regulates  the  E.  M.  F.  of  the  dynamo.  In  cutting 
out  this  regulating  resistance,  the  maximum  E.  M.  F.  at  the 
given  speed  is  obtained  while  the  minimum  E.  M.  F.  obtaina- 
ble is  limited  by  the  total  resistance  of  the  regulating  coil. 
By  specifying  the  percentage  of  extra-resistance  in  circuit  at 
normal  load,  and  the  total  resistance  of  the  coil,  any  desired 
range  may  be  obtained;  see  §  103. 

Designating  the  given  percentage  of  extra-resistance  by  r^ , 
the  total  energy  absorbed  in  the  shunt-circuit,  consisting  of 
magnet  winding  and  regulating  coil,  can  be  expressed  by: 

where 

Psh  —  ~  SM  =  energy  absorbed  in  the  magnet  winding  alone. 
75 

The  potential  between  the  field  terminals  of  a  shunt  dynamo 
being  equal  to  the  E.  M.  F.  output,  E,  of  the  machine,  the 
current  flowing  through  the  shunt-circuit  is: 

P< 
/8h=  -J1,     (313) 

383 


DYNAMO-ELECTRIC  MACHINES.  [§  101 


and  the  number  of  shunt  turns,  therefore  : 

AT       AT*  E 


ysh 


By  means  of  formulae  (289)  to  (292),  which  apply  equally 
well  to  shunt  as  to  series  windings,  the  approximate  mean 
length  of  one  turn  is  found,  and  the  latter  multiplied  by  the 
number  of  turns  gives  the  total  length  of  the  shunt  wire: 


.-.(315) 


By  Ohm's  Law  we  next  find  the  total  resistance  of  the  shunt- 
circuit  at  normal  load,  viz.: 


75    • 

This  contains  the  rx  per  cent,  of  extra  resistance;  in  order  to 
obtain  the  resistance  of  the  shunt  winding  alone,  r"sh  must  be 
decreased  in  the  ratio  of 


and  we  have: 
r'*  =  r'*  X 


—  X     M  X  x * 


x — I ,     (317) 


75  \^          iooy  '    ioo 

which  is  the  resistance  of  the  magnet  winding  when  hot,  at 
a  temperature  of  (15.5  -f  6m)  degrees  Centigrade;  the  magnet 
resistance,  cold,  at  15.5°  C.,  consequently,  is: 


'  8Q  "  i  +  .004  x 


101]  SHUNT    WINDING.  385 

E*  i  i 


;rx. +  ,....  xv (3la) 


&**?#>*;  -+-^ 

The  division  of  (315)  by  (318),    then,   furnishes   the   specific 
length  of  the  required  shunt  wire: 


i    -  * 

911 


=       x       x     '  +          x   '  +  -°°4  x 


The  size  of  the  shunt  wire  can  then  be  readily  taken  from 
a  wire-gauge  table;  if  a  wire  of  exactly  this  specific  length  is 
not  a  standard  gauge  wire,  either  a  length  of  Zsh  feet  of  the 
next  larger  size  is  to  be  taken,  and  the  difference  in  resistance 
made  up  by  additional  extra-resistance,  or  such  quantities  of 
the  next  larger  and  the  next  smaller  gauge  wires  are  to  be 
combined  as  to  produce  the  required  resistance,  rsh,  by  the 
correct  length,  Zsh.  To  fulfill  the  latter  condition,  the  geo- 
metrical mean  of  the  specific  lengths  of  the  two  sizes  must 
correspond  to  the  result  obtained  by  formula  (319);  thus,  if 
X'tto  is  the  specific  length  of  one  size  of  wire  and  A"sh  that  of 
the  other,  such  proportions,  Z'sh  and  Z"8h,  of  the  total  length, 
Zsh  =  Z'sh  -f  Z"sh>  are  to  be  taken  of  each  that: 

^'8h  X  Z'gh  -}-  A"8h  x  Z"sh 


Since  in  this  equation  every  term  contains  a  length  as  a  factor, 
any  length,  for  instance  Z'sh,  may  be  unity,  and  we  have: 


*'*  +  **(£) 


from  which  follows  the  proper  ratio  of  the  lengths  of  the  two 
wires: 


DYNAMO-ELECTRIC  MACHINES.  [§  1O1 

If  the  two  sizes  are  combined  by  their  weight,  the  specific 
weights,  in  pound  per  ohm,  are  to  be  substituted  for  the 
specific  lengths  in  the  above  equations. 

The  sectional  area  of  the  shunt  wire  which  exactly  furnishes 
the  requisite  magnetizing  power  at  the  given  voltage  between 
field  terminals,  with  the  prescribed  percentage  of  extra- 
resistance  in  circuit,  and  at  the  specified  increase  of  magnet 
temperature,  may  be  directly  obtained  by  the  formula: 

<?sh2  =  io.5  X  A8h 


X  ^  X  /T  X  ( i  +  ^  )  x  (i  +  .004  x  U  (322) 

In  the  above  formulae,  E  is  the  E.  M.  F.  supplying  the 
shunt  coils  of  one  magnetic  circuit,  and'  is  identical  with  the 
terminal  voltage  of  the  machine,  if  the  shunt  coils  are 
grouped  in  as  many  parallel  rows  as  there  are  magnetic  cir- 
cuits. But  if  the  number  of  parallel  shunt-circuits  differs 
from  the  number  of  magnetic  circuits,  the  output  E.  M.  F.  of 
the  machine,  in  order  to  obtain  the  proper  value  of  E  for  cal- 
culating the  shunt  winding,  must  be  multiplied  by  the  ratio  of 
the  former  to  the  latter  number. 

The  size,  or  sizes,  of  the  shunt  wire  thus  being  decided 
upon,  by  means  of  formulae  (319)  or  (322),  the  actual  value  of 
>$m,  and  therefrom  the  real  length  of  the  mean  turn  is  to  be 
computed  (see  formulae  (289)  to  (291)),  and  to  be  inserted  into 
formulae  (319),  or  (322),  respectively. 

In  case  of  two  sizes  of  wire  being  used,  the  winding  depth 
can  with  sufficient  accuracy  in  most  cases  be  found  by  means 
of  the  formula: 

(*'*)'  +  (L^\  x  (*•_)• 


which,  however,  on  account  of  the  fact  that  the  mean  length 
of  a  turn  of  the  one  size  of  wire  is  different  from  that  of  the 
other,  and  that,  therefore,  the  ratio  of  the  number  of  turns  of 
the  two  sizes  differs  from  the  ratio  of  their  length,  is  only 
approximately  correct  and  gives  accurate  results  in  case  of 


§101] 


SHUNT    WINDING. 


387 


comparatively  long  and   shallow  coils  only.     For  short  and 
deep  coils,  Fig.  311,  the  heights  of  the  winding  spaces  forThe 


(___£ 

i         !  d 


.6    a  IS 

"  T 

Fig.  311.  —  Dimensions  of  Shunt  Coil. 

two  sizes  are  to  be  separately  determined  by  formula  (257), 
thus: 


h      - 
'lm  — 


-  h'    4-h"          J™  Z/*h  X  dV    .  d'^ 
—  »  »  -f-  »  »  —   A  /  -  ;  -  -+-  •  - 

V  /m    X    7t  4 


where  hm  =  total  height  of  winding  space,  in  inches; 

h'm  and  h"m  =  partial  heights  of  winding  space  occu- 
pied by  wire  of  first  and  second  size, 
respectively; 

6'A  and  tf"sh  =  diameters  of  insulated  shunt  wires,  inch; 
Z'8h  and  Z"8h  —  total  length  of  the  two  sizes  of  wire,  in 

feet; 

</'m  =  internal  diameter  of  coil  formed  by  first 
size   of   wire    (=  core-diameter    plus 
insulation),  in  inches; 
d"m  =  d'm  +  2  h'm  =  £>m-2  h"m- 

=  external  diameter  of  coil  of  first  size  of 
wire,  identical  with  internal  diam- 
eter of  coil  of  second  size,  in 
inches; 

/m  =  length  of  coil,  in  inches;  if  there  is 
more  than  one  coil  in  each  magnetic 
circuit,  /m  is  the  total  length  of  all 
the  coils  in  one  circuit. 


DYNAMO-ELECTRIC  MACHINES.  [§  1O2 

102.  Computation  of  Resistance  and  Weight  of  Magnet 
Winding. 

To  complete  the  calculation  of  the  magnet  winding,  it  is 
necessary  to  find  its  actual  resistance  and  its  weight. 
For  the  resistance  in  ohms  we  have  : 

rm  =  Length  x  ohms  per  foot 

=  Lm  X   (10.5  X   ~)  =  10.5  X  ^ 

=  I0.5X^  =  .875X_^,     -(325) 


in  which  Nm  =  total    number   of   series,    or   shunt    turns    on 

magnets,  formula  (287)  or  (314); 
/t  —  mean  length  of  one  turn,  in  feet; 
/T  =  mean  length  of  one  turn,  in  inches,   formulae 

(289)  to  (292); 
Zm  =  total  length  of  magnet  wire,  in  feet,   formula 

(288)  or  (315); 

tfm2  =  sectional    area    of    magnet   wire,    in    circular 
mils,  formula  (296)  or  (322). 

The  weight  of  the  magnet  winding  is  the  product  of  the  total 
length  of  wire  by  its  specific  weight,  in  pounds  per  foot,  the 
former  being  the  product  of  number  of  turns  and  mean  length 
of  turn,  and  the  latter  being  obtainable  from  the  wire-gauge 
table.  In  order  to  express  the  weight  of  the  winding  by  the 
data  known  from  previous  calculations,  we  proceed  as  follows: 

Weight  =  length  in  feet  X  weight  per  foot 

=  constant  X  length  x  specific  length, 

in  which  : 

„  specific  weight       pounds  per  foot 

Constant  =  -       ..         s  .    —  *—  —  - 

specific  length  feet  per  ohm 

_  ohms  X  pounds 
(feet)2 

/ohms  per  mil  -ft.  X-T^—  «^J  X(lbs.  p.  cu.  in.  xin.  Xsq.  ins.) 

(feet)2  •' 


§  102]  SHUNT    WINDING.  389 


and  particularly  for  copper: 
Constant 


7t 

cir.  mils  X  - 


/  feet      \       /  "4 

/  I0>5  X  -^V  )  X  (  .316  X  feet  X  12  X  - 

\  cir.  mils  /      1°  1,000,000 

(feel)^ 
10.5  X  .316  X  12  X  I  dr   mils 

y      ^ '  —     ?T      ? 

/N    /f .i_\2  vx    ~          ~,:i,,          «-*    *v? 


1,000,000  (feet)2  X  cir.  mils 

The  desired  formula  for  the  bare  weight,  in  pounds,  of  any 
magnet  winding,  therefore,  is: 

Wtm  =  31.3  x  io-6  x  Nm  x  /t  x  Am,  ....(326) 

where  Nm  =  total  number  of  series,   or  shunt  turns  on  mag- 

nets; 

/t  =  mean  length  of  turn,  in  feet; 

Am  =  specific  length  of  magnet  wire,  in  feet  per  ohm, 
formula  (295)  or  (319). 

Writing  (326)  in  the  form 

3 
wtm  =  31.3  X  io-  X 


and    multiplying   both    numerator   and   denominator   by    the 
square  of  the  current  flowing  in  the  magnet  wire,  we  obtain: 

amp.2  X  feet3 


=  31-3  X   io-6  X 

/a 
3L3  X   (- 


amp.2  X  ohms' 
or: 


/  ampere-feet  V 

I  IOOO  I 


^,ra_  ,     (327) 

watts 

which  agrees,  substantially,  with  formula  (275),  §  96.  The 
denominator  of  equation  (327),  since  the  specific  length  of  the 
magnet  wire  in  (326)  is  given  at  15.5°  C.,  represents  the  energy 
lost  in  the  magnets  at  that  temperature,  that  is,  the  actual 
energy  consumption,  at  the  final  temperature  (15.5  +  0m),  of 
the  magnet  winding,  divided  by  (i  -f  .004  x  em);  hence  the 
weight  of  bare  magnet  wire  necessary  to  produce  a  given  mag- 


39°  DYNAMO-ELECTRIC  MACHINES.  [§106 

netizing  force,  AT,  at  a  specified  rise,  0m,  of  the  magnet  tem- 
perature: 


/^r 

I         IO 


1000 

w/m=  31-3  X-V-;      -^-x  (i  +  .004  x  em),  (328) 

—  v    S1 

75 

in  which  AT  =  number  of  ampere-turns  required; 
/t   =  mean  length  of  one  turn,  in  feet; 
0m  =  specified   rise   of  temperature,   in  Centigrade 

degrees; 
S^  =  radiating  surface  of  magnets,  in  square  inches. 

In  case  of  a  compound  winding,  (328)  will  give  the  weights 
of  the  series  and  shunt  wires,  respectively,  if  AT  is  replaced 
by  AT^and  ATah,  and  if  the  energies  consumed  by  each  of 
the  two  windings  individually  are  substituted  for  the  total 
energy  loss  in  the  magnets. 

By  transformation,  the  above  formula  (328)  can  be  employed 
to  calculate  the  temperature  increase  0m,  caused  in  exciting  a 
magnetizing  force  of  AT  ampere-turns  by  a  given  weight,  wtm 
pounds,  of  bare  wire  filling  a  coil  of  known  radiating  surface, 
SK  square  inches.  Solving  (328)  for  0m,  we  obtain: 


(329) 


The  weight  of  copper  contained  in  a  coil  of  given  dimen- 
sions is: 

«*m    =   4    X    /'m    X   hm    X    .21  ,      (330) 

where  /T     =  mean  length  of  one  turn,  in  inches; 
/'m  =  length  of  coil,  in  inches; 
hm  =  height  of  winding  space,  in  inches; 
.21  =  average  specific  weight,  in  pounds  per  cubic  inch, 
of  insulated  copper  wire,  see  Table  XCII.,  §  96. 

103.  Calculation  of  Shunt  Field  Regulator. 

The   voltage   of  a   shunt-wound  machine   is   regulated    by 
means  of  a  variable  rheostat  inserted  into  the  shunt-circuit. 


[3'-3x(^)V£| 

wtm  —  .004  x  [31-3  x  [ — -*_j\  x  -M  1 

L  \      1000      /        ^MJ 


§  103]  SHUNT    WINDING.  391 

The  total  resistance  of  this  shunt  regulator  must  be  the  sum 
of  the  resistances  that  are  to  be  cut  out  of,  and  added-  to,  the 
shunt-circuit  in  order  to  effect,  respectively,  an  increase  and  a 
decrease  of  the  exciting  current  sufficient  to  cause  the  normal 
E.  M.  F.  to  rise  and  fall  to  the  desired  limits.  The  amount 
of  regulating  resistance  required  to  produce  a  given  maximum 
or  minimum  E.  M.  F.  is  obtained,  in  per  cent,  of  the  magnet 
resistance,  by  determining  the  additional  ampere-turns  needed 
for  maximum  voltage,  or  the  difference  between  the  magnet- 
izing forces  for  normal  and  for  minimum  voltage  respectively, 
for,  the  magnetic  flux,  and  with  it  the  magnetic  densities  in 
the  various  portions  of  the  magnetic  circuit,  must  be  varied  in 
direct  proportion  with  the  E.  M.  F.  to  be  generated. 

If  the  dynamo  is  to  be  regulated  between  a  maximum 
E.  M.  F.,  £'m&x  y  and  a  minimum  E.  M.  F.,  £'min,  the  magnet- 
izing forces  required  for  the  resulting  maximum  and  minimum 
flux  are  found  as  follows: 

The  exciting  power  required  for  the  air  gaps  varies  directly 
with  the  field  density,  hence  the  maximum  magnetizing  force, 
by  (228): 

X 


and  the  minimum  magnetizing  force: 

nt"     —     -2T-2?   v    I  TP"    v         mm    \  v  7" 
**'  e  —  •3I33  X  I  t«-     X  — r,7—  I  X  /  g  • 


The  values  of  l"K  in  these  formulae  may  differ  from  each 
other,  and  also  from  that  for  normal  voltage,  owing  to  the 
fact  that  the  product  of  field  density  and  conductor  velocity 
may  have  increased  or  decreased  sufficiently  to  influence  the 
constant  £13  in  formula  (166).  For  each  value  of  3C",  there- 
fore, Table  LXVI.,  §  64,  must  be  consulted. 

For  the  iron  portions  of  the  magnetic  circuit  the  specific 
magnetizing  forces  for  the  new  densities  are  to  be  found  from 
Table  LXXXVIII.,  §  88,  and  to  be  multiplied  by  the  length  of 
the  path  in  the  frame;  thus,  for  maximum  voltage: 


392  DYNAMO-ELECTRIC  MACHINES.  [§103 

and  for  minimum  voltage: 


at"    = 


The  magnetizing  force  required  to  compensate  the  armature 
reactions,  finally,  is  affected  by  the  change  of  density  in  the 
polepieces,  the  latter  determining  the  constant  /£]B  in  formula 
(250);  in  calculating  the  compensating  ampere-turns  for  the 
maximum  voltage,  the  value  of  £15  from  Table  XCI.  is  to  be 
taken  for  a  density  of 

EV 

fail      ^    -P*  max 

p          £'    ' 
and  in  case  of  the  minimum  voltage,  for  a  density  of 


min 


E 
lines  per  square  inch. 

Having  determined  the  maximum  and  minimum  magnetizing 
forces  for  the  various  portions  of  the  circuit,  their  respective 
sums  are  the  excitations,  ATm&y,  and  ATmin,  needed  for  the 
maximum  and  minimum  voltage.  The  number  of  turns  be- 
ing constant,  the  magnetizing  force  is  varied  by  proportion- 
ally adjusting  the  exciting  current,  and  this  in  turn  is  effected 
by  inversely  altering  the  resistance  of  the  field  circuit.  The 
excitation  for  maximum  voltage  is 


AT 

times  that  for  normal  load,  hence  the  corresponding  minimum 
shunt  resistance,  that  is,  the  resistance  of  the  magnet  winding 
alone,  must  be 

AT 


times  the  normal  resistance  of  the  shunt-circuit,  or,  the  extra 
resistance  in  circuit  at  normal  load  is: 


AT^-AT 

X  - 


§  103]  SHUNT    WINDING.  393 

per  cent,   of  the  magnet  resistance.     The  magnetizing  force 
for  minimum  voltage,  similarly  being 


AT 

times  that  for  normal  output,  the  maximum  shunt  resistance  is 

AT 


times  the  normal,  or,  regulating  resistance  amounting  to 


100  X 


per  cent,  of  the  normal  resistance,  which  is 

mM   .        A  7  yog 

A   T>  IX  A  f 


per  cent,  of  the  magnet  resistance,  is  to  be  added  to  the  nor- 
mal shunt  resistance  in  order  to  reduce  the  E.  M.  F.  to  the 
required  limit.  Expressing  the  sum  of  these  percentages  in 
terms  of  the  magnet  resistance,  we  obtain  the  total  resistance 
of  the  shunt  regulator: 

—AT      AT  AT  —  A  Tmin  \        ,      /ooi\ 

—~  -*'*•  (^ 


AT 

This  resistance  is  to  be  divided  into  a  number  of  subdi- 
visions, or  "  steps,"  said  number  to  be  greater  the  finer  the 
degree  of  regulation  desired.  Since  the  shunt-current  de- 
creases with  the  number  of  steps  included  into  the  circuit, 
material  can  be  saved  by  winding  the  coils  last  in  circuit  with 
finer  wires  than  the  first  ones.  At  the  maximum  voltage  the 
shunt-current,  by  virtue  of  Ohm's  Law,  is: 


(332) 

sh 

and  at  minimum  voltage  we  have  : 

•  JT> 

(^h)min  =  —,  -       i—  ,      ...........  (333) 

rsh  -T  rr 

the  current  capacity  of  any  coil  of  the  regulator,  therefore,  can 
with  sufficient  accuracy  be  determined  by  proper  interpolation 


394  DYNAMO-ELECTRIC  MACHINES.  [§103 

between  the  values  obtained  by  formula  (332)  and  (333). 
Thus,  the  current  passing  through  the  shunt-circuit  when 
«x  coils  of  the  regulator  are  contained  in  the  same,  is  found  : 

/  T-    \  I  T    \  i      \/    vXsh/max          V.-'sh/min          /OO4\ 

(Ah)x  =  (Ahjmax  —  nx  X    -  -  ,       (3d4r) 

nr 

where  nr  is  the  total  number  of  the  coils,  or  steps,  of  the  reg- 
ulator. From  (334)  we  obtain  by  transposition: 


VXsh/max  ^/ 

=   <r    v  -  7y^  -  X 

V-'shjmax    ~  '     V/shJmin 


the  latter  formula  giving  the  number  of  coils  which  must  be 
added  to  the  magnet  winding  in  order  to  cause  any  given  cur- 
rent, (/sh)x>  to  flow  through  the  shunt-circuit. 


CHAPTER  XXII. 

COMPOUND    WINDING. 

104.  Determination  of  Number  of  Shunt   and   Series 
Ampere-Turns. 

Since  in  a  compound  dynamo  the  series  winding  is  to  supply 
the  excitation  necessary  to  produce  a  potential  equal  to  that 
lost  by  armature  and  series  field  resistance,  and  by  armature 
reaction,  the  number  of  shunt  ampere-turns  for  a  compound- 
wound  machine  is  the  magnetizing  force  needed  on  open 
circuit,  and  the  number  of  series  ampere-turns  required  for 
perfect  regulation  is  the  difference  between  the  excitation 
needed  for  normal  load  and  that  on  open  circuit.  The  proper 
number  of  shunt  and  series  ampere-turns  can,  therefore,  be 
computed  as  follows: 

The  useful  flux  required  on  open  circuit  is  that  number  of 
lines  of  force  which  will  produce  the  output  E.  M.  F.,  E,  of 
the  dynamos,  viz.  : 

_  6  X  »'B  X  E  X  io9 

*^  **     —~" 


O  AT      \/      AT"  > 


hence  the  ampere-turns  needed  to  overcome,  on  open  circuit, 
the  reluctances  of  air  gaps,  armature  core,  and  magnet  frame, 
respectively,  are: 


=  -3133  x  -^  x 


and 
atm    = 


No  current  flowing  in  the  armature,  there  is  no  armature  re- 
action on  open  circuit,  and  no  compensating  ampere-turns  are 

395 


396  DYNAMO-ELECTRIC  MACHINES.  [§  104 

therefore  needed;  consequently  the  total  number  of  ampere- 
turns  on  open  circuit,  to  be  supplied  by  shunt  winding,  is: 

Next  a  similar  set  of  calculations  is  made  for  the  normal 
output: 

Useful  flux  at  normal  output: 

0  =  6  X  *'p  X  E  X  io9 

where  E'  —  E  +  / '  r'&  +  /r'se,  for  ordinary  compound  wind- 
ing; see  (19),  §  14 

and  E  —  E  -\~  I'  X  (r'&  +  r'se),  for  long  shunt  compound 
winding;  see  (22),  §  14. 

Since,  however,  1  and  /'  are  very  nearly  alike,  E  is  practi- 
cally the  same  in  either  case.  Besides,  E  can  only  be  approxi- 
mately determined  at  this  stage  of  the  calculation,  since  the 
series  field  resistance  is  not  yet  known.  Taking  the  latter  as 
.25  of  the  armature  resistance,  we  therefore  have  for  either 
kind  of  a  compound  winding: 

E  =  E  +  ..25  T  /. ..(337) 

In  case  the  machine  is  to  be  over  compounded  f  or  loss  in  the 
line,  the  percentage  of  drop — usually  5  percent. — is  to  be  in- 
cluded into  the  output  E.  M.  F.,  hence  the  total  E.  M.  F. 
generated  at  normal  load,  for  5  per  cent,  overcompounding: 

E  =  1.05.0+  i.25/V'a (338) 

The  magnetizing  forces  required  at  normal  load,  then,  are: 

<***  =  -3133  X  TT-X  l\\ 


t   -k 

*r     -    At 

14 


_ 

180 


§  104] 


COMPOUND    WINDING. 


397 


Their  sum  is  the  total  number  of  ampere-turns  needed  for 
excitation  at  normal  output: 


A  T  = 


at 


this  is  supplied  by  shunt  and  series  winding  combined,   conse- 
quently the  compounding  number  of  series  ampere-turns: 

A  Tse  =  A  T  -  A  Tsh  =  A  T  -  A  T0 (339) 

In  the  above  formulae  for  at^o  and  atm ,  the  factors  A0  and  A 
are  the  leakage  coefficients  of  the  machine  on  open  circuit  and 


r 

I     I  s?\  I     ) 


Figs.   312  and  313. — Positions  of  Exploring  Coils  for  Determining  Distribu- 
tion of  Flux  in  Dynamos. 

at  normal  load,  respectively.  Although  the  effect  of  the 
armature  current  upon  the  distribution  of  the  magnetic  flux  in 
the  different  parts  of  the  machine  is  very  marked,  as  shown 
by  tests  made  by  H.  D.  Frisbee  and  A.  Stratton, '  the  ratio  of 
the  total  leakage  factors  in  the  two  cases,  especially  in  com- 
pound-wound machines,  is  so  small  that  the  factor  A,  as  obtained 
from  formulae  (157),  can  be  used  for  the  calculation  of  both  the 
shunt  and  the  total  ampere-turns.  Since,  however,  it  is  very 
instructive  to  note  the  actual  difference  between  the  distribu- 
tion of  the  magnetic  flux  at  normal  output  and  that  on  open 
circuit,  the  results  of  the  tests  mentioned  above  are  compiled 
in  the  following  Table  XCV.,  in  which  all  the  flux  intensities 
in  the  various  parts  of  the  different  machines  experimented 
upon  are  given  in  per  cent,  of  the  useful  flux  through  the 


'  "The  Effect  of  Armature  Current  on  Magnetic  Leakage  in  Dynamos  and 
Motors,"  graduation  thesis  by  Harry  D.  Frisbee  and  Alex.  Stratton,  Columbia 
•College  ;  Electrical  World,  vol.  xxv.  p.  200  (February  16,  1895). 


D  YNA MO-ELECTRIC  MA  CHINES. 


[§104 


1C  »O  CO  1O 


si 


»O  1C     1O 

§I>00>OG6CO1O      t-         TH 


111 

^ 


ill 


SB 


"3  * 

It 


S<M10^J>GOO     CO        TH 
(N   TH    C2    TH    TH    TH         50  «0 


§O 
CQ 


10        10 

TH     -THOOS 


10  10  CO10- 

«DGO<M     OO        CO     (MCQCO 

—  lOrH       10  «0  Tt^ 


i  L  & 

Mil  tl 

*  a   s« 

CO 


1  11  II  1 

iirispi1  a  il 

QJ^^HcSgH^  CM  g® 
^00^^^^  0  0  ^^ 
5fcH^0000  ^  ^  <£<£ 

I11.S.S.2.S   |     | 
o  o  o    ^      "^ 
O      O 


<jfflfflobPQ  W    W 


CO        10 
CO     Ci^GOio'     • 

OS  ,-<«0-- 


*T- 

a  la 

|!I 
§8.^ 

gSS1 

111 

O   O>  «t_i 
11.0 

JII 


§  105]  COMPOUND    WINDING.  399 

armature,  the  various  positions  of  the  exploring  coils  being 
shown  in  the  accompanying  Figs.  312  and  313.  Appended  to 
this  table  are  the  respective  leakage  factors,  obtained  in  divid- 
ing for  each  case  the  maximum  percentage  of  flux  by  100,  and 
also  the  ratios  of  the  leakage  factor  at  normal  output  to  that  on 
open  circuit. 

105.    Calculation   of    Compound    Winding    for    Given 
Temperature  Increase. 

After  having  determined  the  number  of  shunt  and  series 
ampere-turns  giving  the  desired  regulation,  the  calculation  of 
the  compound  winding  itself  merely  consists  in  a  combination 
of  the  methods  treated  in  Chapters  XX.  and  XXI. 

The  total  energy  dissipation,  JPmi  allowable  in  the  magnet 
winding  for  the  given  rise  of  0m  degrees  being  obtained  from  for- 
mula (283),  this  energy  loss  is  to  be  suitably  apportioned  to  the 
two  windings,  preferably  in  the  ratio  of  their  respective  mag- 
netizing forces,  so  that  the  amount  to  be  absorbed  by  the 
series  winding  is: 

AT1  AT1          9 

^«  -  ^~  X  -s  X  S«  watts;      (340) 


AT 
hence,  by  (294),  the  resistance  of  the  series  winding,  at  15.5°  C. : 

_  Ae  i 

rm    -  js       i  -|-  .004  x  6m 


AT        75  ~/2    N  i+.oo4X«m' 
The  number  of  series  turns  being  readily  found  from 

^se  =  *£yk 

the  total  length  of  the  series  field  conductor  is: 

/',       AT^       /'T 

/         —     1\/        'y    __  V  TPAt* 

-*-/gg     —    J»  V  gQ     /\  —  /\  ICCLj 

and  this,  divided  by  the  series  field  resistance,  furnishes  the 
specific  length  of  the  required  series  field  conductor,  thus: 


400  DYNAMO-ELECTRIC  MACHINES.  [§  106 

I'          AT  72 

-       X 


//  T7  V    /    V    /' 

=  6.25  X  -  Vve  X  (i  +  .004  X  8m),     .....  (342) 

•^M      X^m 

where  /'T  =  mean  length  of  one  series  turn,  in  inches. 

The  sectional  area  of  the  series  field  conductor,  therefore, 
analogous  to  (296),  is: 

#se2  =  10.5  X  Ase 

A  T  v  /  v  /' 

=  65  x  -     x     *    T  x  (i  +  .004  x  »m)  ......  (343) 

°M   A     m 

If  one  single  wire  of  this  cross-section  would  be  impractical, 
one  or  more  cables  stranded  of  nM  wires,  each  of 


circular  mils,  may  be  used,  or  a  copper  ribbon  may  be  em 
ployed. 

The  actual  series  field  resistance,  at  15.5°  C.,  then  being: 


Ac  7Vse  x  H 

rse  =  10.5   X  -rni  =  10.5  X  -  — 5-5— 


IV     v  /'  A/"    v  /' 

=  .875  x       -i-1  =  .875  x       * 


y  ($'   V 

A    Vu  se; 

the  actual  energy  consumption  in  the  series  winding  is: 

•^se  —  -*       X    ^  se 


and,   consequently,  the  energy  loss  permissible  in  the  shunt 
winding: 


KX  (i  +.004  X  «m)  ......  (346) 

If  the  extra-resistance  at  normal  load  is  to  be  r^  per  cent. 
of  the  shunt  resistance,  the  total  watts  consumed  by  the  entire 


§  105]  COMPOUND    WINDING.  401 

shunt-circuit  can  be  obtained  by  (312);  formulae  (313)  to  (317) 
then  furnish  the  number  of  shunt  turns,  the  total  length, 
and  the  resistance  of  the  shunt  wire,  and  from  (318)  and  (319) 
the  specific  length  and  the  sectional  area  are  finally  received: 


x 


=  .875  x          x  /',  x       +  ~      x(i+.oo48m)  (348) 


In  estimating  the  mean  lengths  of  series  and  shunt  turns, 
/'T  and  /"T  ,  respectively,  all  depends  upon  the  manner  of  plac- 
ing the  field  winding  upon  the  cores.  If  the  winding  is  per- 
formed by  means  of  two  or  more  bobbins  upon  each  core,  the 
series  winding  filling  one  spool,  preferably  that  nearest  to  the 
brush  cable  terminals,  and  the  shunt  winding  occupying 
the  remaining  ones,  then  the  approximate  mean  length,  /'T,  of 
one  series-turn  is  equal  to  that  of  one  shunt  turn,  /"T,  and  also 
identical  with  the  average  turn,  /T,  given  by  Tables  LXXX., 
§  83,  and  XCIV.,  §  99.  But,  if  the  field  coils  are  wound  directly 
upon  the  cores  —  the  series  winding  usually  being  wound  on 
first  —  the  lengths  /'T  and  /"T  differ  from  each  other,  and  can  be 
approximately  determined  by  apportioning  from  J-  to  ^  of 
the  average  winding  height,  given  in  Table  LXXX.,  to  the 
series  winding,  and  the  remainder  to  the  shunt  winding. 


TAKT  VII . 


EFFICIENCY     OF     GENERATORS     AND 

MOTORS. 
DESIGNING  OF  A  NUMBER   OF    DYNAMOS 

OF  SAME  TYPE. 
CALCULATION     OF     ELECTRIC     MOTORS, 

UNIPOLAR    DYNAMOS, 

MOTOR-GENERATORS,   ETC. 

DYNAMO-GRAPHICS. 


CHAPTER  XXIII. 

EFFICIENCY    OF    GENERATORS    AND    MOTORS.  l 

106.  Electrical  Efficiency, 

The  electrical  efficiency,  or  the  economic  coefficient  of  a  dynamo, 
is  the  ratio  of  its  useful  to  the  total  electrical  energy  in  its 
armature,  the  latter  being  the  sum  of  the  former  and  of  the 
energy  losses  due  to  the  armature  and  field  resistances;  hence 
the  electrical  efficiency  of  a  generator  : 


and  that  of  a  motor  : 

^PF=f-(P*p+P*\    ......  (850) 

where  %    =  electrical  efficiency  of  machine; 

P   —  electrical  energy,  at  terminals  of  machine; 

P'  =  electrical  activity  in  armature,   or  total   energy 

engaged  in  electromagnetic  induction; 
P&  =  energy  absorbed  by  armature  winding; 
/>M  =  energy  used  for  field  excitation. 

In  case  of  a  generator,  P  is  the  output  available  at  the 
brushes,  while  in  a  motor  it  is  the  total  energy  delivered  to 
the  terminals,  that  is,  the  intake  of  the  motor. 

Inserting  into  (349)  and  (350)  the  expressions  for  P,  PM  and 
-PM  in  terms  of  E.  M.  F.  current-strength  and  resistance,  the 
following  formulae  for  the  electrical  efficiency  are  obtained: 

Series-wound  generator: 

'    ...............  (351) 


1  See  "Efficiency  of  Dynamo-Electric  Machinery,"  by  Alfred  E.  Wiener 
American  Electrician,  vol.  ix.  p.  259  (July,  1897). 


406  DYNAMO-ELECTRIC  MACHINES.  [§  1O7 

Shunt-wound  generator: 

E  I 


a  <r" 
^  sh 


Compound-wound  generator: 

*7e  =    J?  T     \      T>*  (-•       \     y<     \      I      /    a  ^     J        '  '  '  '  (353) 

&1  -\-  1      (r  a  -f-  r  se)  4-  ysh  /•  sh 
Series-wound  motor: 

*=*/-/;g<r-+r'-);  ............  (354) 

Shunt-wound  motor: 

El-  (/'a^a  +  /shVV) 


Compound-wound  motor: 


Since  the  electrical  energy  does  not  include  waste  by  hyster- 
esis, eddy  currents,  and  friction,  but  is  depending  upon  the 
energy  losses  due  to  heating  by  the  current  only,  it  may  be 
adjusted  to  any  desired  value  by  properly  proportioning  the 
resistances  of  the  machine;  see  formulae  (10),  (13),  (20),  and 
(23),  §  14.  The  electrical  efficiency  of  modern  dynamos  is 
very  high,  ranging  from  %  =  .75,  or  75  per  cent.,  for  small 
machines,  to  as  high  as  7/e  =  .99,  or  99  percent.,  for  very  large 
generators. 

107.  Commercial  Efficiency. 

By  the  commercial  or  net  efficiency  of  a  dynamo-electric 
machine  is  meant  the  ratio  of  its  output  to  its  intake.  The 
intake  of  a  generator  is  the  mechanical  energy  required  to 
drive  it,  and  is  the  sum  of  the  total  energy  generated  in  the 
armature  and  of  the  energy  losses  due  to  hysteresis,  eddy  cur- 
rents, and  friction;  the  intake  of  a  motor  is  the  electrical 
energy  delivered  to  its  terminals.  The  output  of  a  generator 
is  the  electrical  energy  disposable  at  its  terminals;  the  output 
of  a  motor  is  the  mechanical  energy  disposable  at  its  shaft,  and 


§107]     EFFICIENCY  OF  GENERATORS  AND  MOTORS.       407 

consists  in  the  useful  energy  of  the  armature  diminished  by 
hysteresis,  eddy  current,  and  friction  losses.  The  commercial 
efficiency  of  a  generator,  therefore,  is : 

_  />  P  P 

'c  ~Dff  D'       I         D'  Dl       I         O          i         D i         O 


A  +  Pe  +  P0  ' 


(357) 


and  that  of  a  motor  : 
p.  _     ^_ 

* 


in  which  77C    =  commercial  or  net  efficiency  of  dynamo; 

P    —  electrical  energy  at  terminals,  /.  *.,  output  of 

generator,  or  intake  of  motor; 
P'    —  electrical  activity  in  armature; 
P"  =  mechanical  energy  at  dynamo  shaft,  i.  e.,  driv- 

ing power  of  generator,  or  mechanical  out- 

put of  motor,  respectively; 
P&  =:  energy  absorbed  by  armature  winding; 
/>M  =  energy  used  for  field  excitation; 
P±  =  energy  consumed  by  hysteresis; 
Pe  =  energy  consumed  by  eddy  currents; 
P0  =  energy  loss  due  to  air  resistance,  brush  fric- 

tion, journal  friction,  etc.  ; 
P'0  —  energy  required  to  run  machine  at  normal  speed 

on  open  circuit. 

Substituting  in  the  above  formulae  the  values  of  P,  PM  and 
PU,  the  following  set  of  formulae,  resembling  (351)  to  (356),  is 
obtained  : 


Series-wound  generator: 

El 


'•  ('*  + 
Shunt-wound  generator: 

El 

T     2    ~< 

sh 


(359) 


El       f"  r          /•  r"  ''       (360) 


498  DYNAMO-ELECTRIC  MACHINES.  [§  107 

Compound-wound  generator: 


Series-wound  motor: 


Shunt-wound  motor: 


El 

Compound-wound  motor: 

-  [/"  K  +  r'K)  + 


In  case  of  belt-driving,  the  mechanical  energy  at  the  dynamo 
shaft,  in  foot-pounds  per  second,  can  also  be  expressed  by  the 
product  of  the  belt-speed,  in  feet  per  second,  and  of  the  effect- 
ive driving  power  of  the  belt,  in  pounds,  or,  converted  into 
watts  : 


=  1.3564  X  J/B  X  C^B  -/B),       ..................  (365) 

where   VE  =  belt  velocity,  in  feet  per  minute; 
V'-Q  =  belt  velocity,  in  feet  per  second; 
FK  =  tension  on  tight  side  of  belt,  in  pounds; 
/B  =  tension  on  slack  side  of  belt,  in  pounds. 

The  commercial   efficiency  of  a  generator,  therefore,  may   be 
expressed  by: 

P  FT 

*•  =  ^  ==  1.3564  x*-.x  (*-,-/,)'    "(366) 

and  the  commercial  efficiency  of  a  motor,  by  : 

.    P"  _     1.3564  X  P'B  X 
- 


The  commercial  efficiency,  T/C,  of  a  dynamo  is  always  smaller 
than  its  electrical  efficiency,  7/e,  since  the  former,  besides  the 
electrical  energy-dissipation,  includes  all  mechanical  and  mag- 


§108]     EFFICIENCY  OF  GENERATORS  AND  MOTORS.       4°9 

netic  energy  losses,  such  as  are  due  to  journal  bearing  fric- 
tion, to  hysteresis,  to  eddy  currents,  and  to  magnetic  leakage.  \ 
The  commercial  efficiency,  therefore,  depends  upon  the 
amount  of  the  electrical  efficiency,  upon  the  shape  of  the 
armature,  upon  the  design,  workmanship,  and  alignment  of 
the  bearings,  upon  the  pressure  of  the  brushes,  upon  the 
quality  of  the  iron  employed  in  its  armature  and  field  magnets, 
and  upon  the  degree  of  lamination  of  the  armature  core;  while 
the  electrical  energy  is  a  function  of  the  electrical  resistances 
only.  The  mechanical  and  magnetical  losses  vary  very  nearly 
proportional  to  the  speed;  the  no  load  energy  consumption 
for  any  speed,  consequently,  is  approximately  equal  to  the 
open  circuit  loss  at  normal  speed  multiplied  by  the  ratio  of 
the  given  to  the  normal  speed. 

The  commercial  efficiency  of  well-designed  machines  ranges 
from  rjc  =  .6,  or  60  per  cent.,  for  small  dynamos,  to  rjc  =  .95,' 
or  95  per  cent.,  for  large  ones. 

Since  in  a  direct-driven  generator  the  commercial  efficiency 
is  the  ratio  of  the  mechanical  power  available  at  the  engine 
shaft  to  the  electrical  energy  at  the  machine  terminals,  for 
comparisons  between  direct  and  belt-driven  dynamos  the  loss 
in  belting  should  also  be  included  into  the  commercial  effi- 
ciency of  the  belt-driven  generator.  The  following  Table 
XCVI.  contains  averages  of  these  losses  for  various  arrange- 
ments of  belts: 

TABLE  XCVI. — LOSSES  IN  DYNAMO  BELTING. 


ARRANGEMENT  OP  BELTS. 

Loss  IN  BELTING 
IN  PER  CENT. 
op  POWER  TRANSMITTED. 

Horizontal  Belt     

5  to  10  per  cent. 

Vertical  Belt  

7  "  12 

Countershaft  and  Horizontal  Belt 

10  "  15       " 

Countershaft  and  Vertical  Belt  

12  "  20 

20  "  30 

108.  Efficiency  of  Conversion. 

The  efficiency  of  conversion,  or  the  gross -efficiency,  is  the  ratio 
of  the  electrical  activity  in  the  armature  to  the  mechanical 
energy  at  the  shaft,  or  vice  versa;  that  is  to  say,  in  a  generator 


4io 


DYNAMO-ELECTRIC  MACHINES. 


[§109 


it  is  the  ratio  between  the  total  electrical  energy  generated 
and  the  gross  mechanical  power  delivered  to  the  shaft,  and  in 
a  motor  is  the  ratio  of  the  mechanical  output  to  the  useful 
electrical  energy  in  the  armature.  Or,  in  symbols,  for  a 
generator: 


P' 

-pn 


P' 


P  +  P&  + 


P'       P' 


(ra 


~  746    /#>  ~ 
and  for  a  motor  : 

P          P'-P' 


X  »'„  X  (^B  -  /B) 


...(368) 


"*  ~      5'    - 


^  7  -    [/'  2(a  +«)  +  /sh2  ^"sh] 

_  746    hp  _  1.3564  X  PB  X  (^B  ~/B). 
~     ^'7'  E'  I' 


...(369) 


The  energy  of  conversion,  ^g ,  is  the  quotient  of  the  com- 
mercial and  electrical  efficiencies,  and  therefore  varies 
between 

rjg  =   •—  =  ~  -  =  .8,  or  80  per  cent, 

*7e  •  75 

for  small  dynamos,  and 

rte  =  —  =  —  =  .96,  or  96  per  cent., 

Ve  -99 

for  large  machines. 

109.  Weight-Efficiency  and  Cost  of  Dynamos. 

As  the  commercial  efficiency  increases  with  the  size  of  the 
machine,"  so  the  weight-efficiency — that  is,  the  output  per  unit 
weight  of  the  machine — in  general  is  greater  for  a  large  than 
for  a  small  dynamo,  and  the  cost  of  the  machine  per  unit  out- 
put, therefore,  gradually  decreases  as  the  output  increases. 

If  all  the  different  sized  machines  of  a  firm  were  made  of  the 


§109]     EFFICIENCY  OF  GENERATORS  AND  MOTORS.       411 

same  type,  all  having  the  same  linear  proportions,  and  if  all 
had  the  same,  or  a  gradually  increasing  circumferential 
velocity,  and  were  all  figured  for  the  same  temperature 
increase  in  their  windings,  then  the  weight-efficiency  would 
gradually  increase  according  to  a  certain  definite  law,  and  the 
cost  per  KW  would  decrease  by  a  similar  law.  In  practice, 
however,  such  definite  laws  do  not  exist  for  the  following 
reasons:  (i)  Up  to  a  certain  output  a  bipolar  type  is  usually 
empl-oyed,  while  for  the  larger  capacities  the  multipolar  types 
are  more  economical;  this  change  in  the  type  causes  a  sudden 
jump  to  take  place,  both  in  the  weight-efficiency  and  in  the 
specific  cost,  between  the  largest  bipolar  and  the  smallest 
multipolar  sizes.  (2)  The  machines  of  the  different  capacities 
are  not  all  built  in  linear  proportion  to  each  other,  but,  in 
order  to  economize  material,  tools,  and  patterns  the  outputs 
of  two  or  three  consecutive  sizes  are  often  varied  by  simply 
increasing  the  length  of  armature  and  polepieces;  in  this  case 
a  small  machine  with  a  long  armature  may  be  of  greater 
weight-efficiency  and  of  a  smaller  specific  price  than  the  next 
larger  size  with  a  short  armature.  (3)  The  conductor-velocity 
is  not  the  same  in  all  sizes;  as  a  general  rule,  it  is  higher  in 
the  bigger  machines,  but  often  the  increase  from  size  to  size 
is  very  irregular,  causing  deviation  in  the  gradual  increase  of 
the  weight-efficiency.  (4)  Certain  sizes  of  machines  being 
more  popular  than  others,  a  greater  number  of  these  can  be 
manufactured  simultaneously,  and  therefore  these  sizes  can  be 
turned  out  cheaper  than  others,  and  the  specific  cost  of  such 
sizes  will  likely  be  smaller  than  that  of  the  next  larger  ones. 
(5)  Large  generators  frequently  are  fitted  with  special  parts, 
such  as  devices  for  the  simultaneous  adjustment  and  raising 
of  the  brushes,  arrangements  for  operating  the  switches, 
brackets  for  supporting  the  heavy  main  and  cross-connecting 
cables,  platforms,  stairways,  etc.,  the  additional  weight  and 
cost  of  these  extra  parts  often  lowering  the  weight  efficiency 
and  increasing  the  specific  cost  beyond  those  of  smaller  sizes 
not  possessing  such  complications.  These  various  considera- 
tions, then,  show  why  prices  differ  so  widely,  and  why  the 
ratio  of  weight  to  output  is  so  varied:  and  they  offer  a  reason 
for  the  fact  that  the  data  derived  from  different  makers'  price- 
lists  are  at  such  a  great  variance  from  each  other. 


412 


DYNAMO-ELECTRIC  MACHINES. 


[§109 


In  the  following  Table  XCVII.  the  author  has  compiled  the 
weights,  list  prices,  weight-efficiencies  (watts  per  pound), 
and  specific  prices  (dollars  per  KW)  for  all  sizes  of  dynamos 
as  averaged  from  the  catalogues  of  numerous  representative 
American  manufacturers  of  high  grade  electrical  machinery: 

TABLE  XCVII. — AVERAGE  WEIGHT  AND  COST  OF  DYNAMOS. 


CAPACITY 

IN 

KILOWATTS. 

AVERAGE 
WEIGHT 
(TOTAL,  NET) 
LBS. 

WEIGHT 

PER 

KILOWATT. 
LBS. 

OUTPUT 
PER  POUND 
WATTS. 

AVERAGE 
PRICE, 
(COMPLETE). 

PRICE 

PKR 

KILOWATT. 

.5 

80 

160 

6.25 

$  50.00 

$100.00 

1 

150 

150 

6.67 

80.00 

8000 

2 

275 

137 

7.3 

125.00 

6250 

4 

500 

125 

8.0 

170.00 

42.50 

6 

700 

117 

8.55 

210.00 

35.00 

10 

1,100 

110 

9.1 

300.00 

30.00 

15 

1,600 

107 

9.35 

412.50 

27.50 

25 

2,600 

104 

9.6 

625.00 

25.00 

50 

5,000 

100 

100 

1,150.00 

23.00 

75 

7,300 

97.3 

10.3 

1,650.00 

22.00 

100 

9,500 

95 

10.5 

2,200.00 

21.50 

150 

14,000 

93.3 

10.7 

3,150.00 

21.00 

200 

18,500 

92.5 

10.8 

4,150.00 

20.75 

300 

27,000 

90 

11.1 

6,150.00 

20.50 

400 

35,000 

87.5 

11.4 

-    8,100.00 

20.25 

500 

42,500 

85 

11.8 

10,000.00 

20.00 

600 

50,000 

83.3 

12.0 

11,850.00 

19.75 

700 

58,000 

82.9 

12.1 

13,650.00 

19.50 

800 

65,000 

81.3 

12.3 

15,400.00 

19.25 

1,000 

80,000 

80 

12.5 

19,000.00 

1900 

1,500 

120,000 

80 

12.5 

27,750.00 

18.50 

2,000 

160,000 

80 

12.5 

36,000.00 

18.00 

Since  the  speeds  for  the  same  outputs  vary  considerably 
with  different  manufacturers,  the  averages  given  in  columns  3 
and  6  above  refer  to  medium,  or  moderate  speeds,  and  must 
be  proportionally  reduced  for  high,  and  increased  for  low 
speeds. 


CHAPTER   XXIV. 

DESIGNING    OF    A    NUMBER    OF    DYNAMOS   OF    SAME    TYPE. 

110.  Simplified  Method  of  Armature  Calculation. 

In  case  a  number  of  different  sizes  of  machines  are  to  be 
designed  of  the  same  type,  the  method  of  calculating  may  be 
materially  simplified  by  subdividing  the  fundamental  formulae 
in  two  parts,  the  one  containing  those  quantities  which  remain 
constant  for  the  type  in  question,  while  the  other  embodies  all 


Fig.  314. — Cross-Section  of  Field  Magnet  and  Rectangle  Inclosing  Armature 

Core. 

factors  that  vary  with  the  output  of  the  machine.  By  adopt- 
ing a  fixed  ratio  between  the  cross-section  of  the  field  magnet 
and  the  area  of  the  rectangle  containing  the  longitudinal 
section  through  the  armature  core,  which  is  perfectly  proper 
for  any  particular  type  of  dynamo,  and  by  basing  all  calcula- 
tions upon  the  density  of  the  magnetic  lines  in  the  magnet 
frame,  Cecil  P.  Poole  -1  has  obtained  a  set.  of  simple  formulae 
which  admit  of  ready  separation  into  a  "  preliminary "  and 
a  "working"  part. 

Representing  the  area  of  the  magnet  frame  by  the  quotient 


1  "  A  Simplified  Method  of  Calculating  Dynamo-Output  and  Proportions,' 
by  Cecil  P.  Poole,  Electrical  Engineer,  vol.  xvi.  p.  483  (December  6,  1893). 

413 


4  1  4  D  YNA  MO-ELE  C  7  'RIC  MA  CHINES.  [§  1  1  0 

of  the  longitudinal  armature  section  and  the  number  of  pairs 
of  poles,  Fig.  314,  thus: 


(370) 


the  E.  M.  F.  generated  in  the  armature  can  be  expressed  by: 
E  =  (B"m  X   (Sm  X  «p)  X  £  X  ~c  X   ~    X  io-8 

T  7\7^  7;       V      T  -7 

A 


m 


V    —    V    //     V    /     V    --1    V       c  V    in" 

'  '       '    X      "~ 


i  TV" 

=  3-82  x  T  x  (B"m  x  4  x  vc  x  V  x  io-8,     —  (371) 

A  72  p 

where     (B"m  =  magnetic  density  in  magnet  cores,  in  lines  per 

square  inch; 

Sm  —  area  of  magnet-core,  in  square  inches; 
d&  =  diameter  of  armature  core,  in  inches; 
/a  =  length  of  armature  core,  in  inches; 
7VC  =  total  number  of  armature  conductors; 
np  =  number  of  pairs  of  magnet  poles; 
n'p  =  number  of  bifurcations  of  current  in  armature; 
JV  =  speed,  in  revolutions  per  minute; 
vc  =  conductor-velocity,  in  feet  per  second; 
A  =  factor  of  magnetic  leakage. 

Expressing  the  length  of  the  armature  core  as  a  multiple  of 
its  diameter: 

4  —  ^is  X  <4  » 

and  writing  for  the  number  of  conductors  on  the  armature  : 

_  d&  n 

•L  v  c    —     P///        X    fl\  , 
°     a 

where     d&  =  diameter  of  armature  core,  in  inches; 

#"'a  =  pitch  of  conductors  on  armature  circumference, 

in  inches; 

«!  =  number  of  layers  of  armature  conductors; 
formula  (371)  becomes: 

E  =  3.82  X  \  X  <B"m  X  vc  X  k»  X  d&  X  ^ 


§110]  DESIGNING  DYNAMOS   OF  SAME    TYPE.  415 

and  by  transformation  we  obtain: 

4  =  2887  Js  x  *  x  *'".  x  »'P       ..(372) 

r  «'.  x  *,.  x  *.  x  «, 

The  pitch,  #"'a,  in  this  formula  depends  upon  the  size  and 
shape  of  the  armature  conductor  and  its  arrangement  upon 
the  armature  core;  it  is,  therefore,  convenient  to  put: 

d'\   =   k»    X    tf'a, 

in    which  #'a  —  insulated    width    of    armature    conductor,    in 

inches;  and 
/&19  —  pitch-factor,  depending  upon  type  of  armature. 

The  factor  /£19,  for  smooth  drum  armatures,  varies  between  1.05 
and  1.2,  according  to  the  spacing  of  the  conductors  on  the 
circumference,  see  Table  XVII.,  §  23;  in  smooth  rings  the 
limits  of  kw  are  i.oi  and  1.25;  for  toothed  armatures  it  ranges 
from  2.05  to  2.2,  if  the  width  of  the  slot  is  equal  to  the  top 
breadth  of  the  tooth;  if  the  latter  is  not  the  case,  these  limits 
must  be  multiplied  by  the  ratio  of  the  pitch  of  the  slots  to 
twice  the  slot  width;  and  for  perforated  armatures  the  value  of 
£19  lies  between  1.5  and  2,  according  to  the  ratio  of  the 
width  of  the  perforations  to  their  distance  apart. 

Uniting  in  (372)  all  the  constant  factors  into  one  quantity 
we  can  write  for  the  working  formula: 


*p>      ..(373) 


in  which  the  constant  has  the  value: 

•    :  K  = 


voi'm  x  *18  x  v0 

If  all  the  dynamos  of  the  type  under  consideration  are  to 
have  the  same  voltage,  the  same  pitch-factor  and  number  of 
layers  of  armature  conductor,  and  are  to  have  their  armatures 
connected  in  the  same  manner,  then  E ',  £19,  n\  and  n'p  are 
constant,  and  may  be  transferred  from  (373)  to  (374),  still 
more  simplifying  the  working  formula,  which  under  these  con- 
ditions becomes: 

d&  =  K'x  vTlTtf7.,     (375) 


4 1 6  D  YNAMO-ELECTRIC  MA  CHINES.  [§  1 1 1 

while  the  corresponding  preliminary  formula  is  : 

K'  =  2887  x  4  / E'  x  n<*  x  k™  . .  (376) 

V     &"m    X    *18    X    Vc    X    »! 

Having  found  the  armature  diameters  for  the  various  sizes, 
their  lengths  can  then  be  readily  obtained  by  multiplication 
with/&18;  and  diameter  and  length  of  the  armature  determine 
the  principal  dimensions  of  the  field  frame. 

The  calculation  of  the  total  magnetizing  force  and  of  the 
field  winding,  for  the  number  of  dynamos  of  the  same  type,  by 
similarly  extracting  from  the  respective  formulae  all  the  fixed 
quantities,  may  also  be  somewhat  simplified,  but  the  direct 
methods  given  for  the  field  calculation  are  already  so  simple 
that  not  much  can  be  gained  by  so  doing,  and  it  is  therefore 
preferable  to  separately  consider  every  single  case. 

111.  Output  as  a  Function  of  Size. 

If  the  ratio  of  the  dimensions  of  two  dynamos  of  the  same 
type  is  i  :  m,  the  ratio  of  their  respective  outputs  can  be 
expressed  as  an  exponential  function  of  this  ratio  of  size,  as 
follows: 


If  the  exponent  x  is  given  for  the  various  practical  condi- 
tions, the  dimensions  of  any  dynamo  for  a  required  output 
can,  therefore,  be  calculated  from  the  dimensions,  and  the 
known  output  of  one  machine  of  the  type  in  question,  from 
the  formula: 

',    (377) 


which  gives  the  multiplier,  by  which  the  linear  dimensions  of 
the  known  machine  are  to  be  altered  in  order  to  obtain  the 
required  output. 

The  author,  by  a  mathematical  deduction, '   has  found  the 
theoretical  value  of  the  required  exponent  to  be  : 
.  #=2.5. 

1  "Relation  Between  Increase  of  Dimensions  and  Rise  of  Output  of 
Dynamos,"  by  Alfred  E.  Wiener,  Electrical  World,  vol.  xxii.  pp.  395  and  409 
(November  18  and  25,  1893)  ;  Elektrotech.  Zeitschr.,  vol.  xv.  p.  57  (February 
I,  1894). 


§  111] 


DESIGNING  DYNAMOS   OF   SAME    TYPE. 


417 


In  the  mathematical  determination  of  x,  however,  the  thick- 
ness of  the  insulation  around  the  armature  conductor  has,  for 
convenience,  been  neglected.  The  theoretical  value  found, 
therefore,  holds  good  only  for  the  imaginary  case  that  the 
entire  winding  space  is  filled  with  copper.  Since  the  per- 
centage of  the  winding  space  occupied  by  insulating  material 
is  the  larger  the  smaller  the  armature,  the  difference  between 
the  actual  and  the  theoretical  output  will  be  the  greater,  com- 
paratively, the  smaller  the  dynamo,  and  it  follows  that  the 
exponent,  x,  varies  with  the  sizes  of  the  machines  to  be 
compared.  Furthermore,  the  area  of  the  armature  conductor 
decreases  with  the  voltage  of  the  machine;  in  a  high-voltage 
dynamo,  therefore,  a  larger  portion  of  the  winding  space  is 
occupied  by  the  insulation  than  would  be  the  case  if  the  same 
machine  were  wound  for  low  tension.  From  this  it  follows  that 
the  output  of  any  dynamo,  if  wound  for  low  voltage,  is  greater 
than  if  wound  for  high  potential,  and  the  value  of  the  expo- 
nent x,  consequently,  also  depends  upon  the  voltages  of  the 
machines  to  be  compared.  Taking  up  by  actual  calculation  the 
influence  of  size  and  of  voltage  upon  the  value  of  x,  the  general 
law  was  found  that  the  exponent  of  the  ratio  of  outputs  of  two 
dynamos  of  the  same  type  increases  with  decreasing  ratio  of 
their  linear  dimensions  as  well  as  with  decreasing  ratio  of  their 
voltages;  the  theoretical  value  being  correct  only  for  the  case 
that  the  dynamo  to  be  newly  designed  is  to  have  10  or  more 
times  the  voltage,  and  at  least  the  8-fold  size  of  the  given 
one.  This  law  is  observed  to  really  hold  in  practice,  as  can 
be  derived  from  the  following  Table  XCVIIL,  which  gives 
average  values  of  the  exponent  x  for  all  the  different  ratios 
of  size  and  voltage: 

TABLE  XCVIII. — EXPONENT  OP  OUTPUT-RATIO  IN  FORMULA  FOR  SIZE- 
RATIO  FOR  VARIOUS  COMBINATIONS  OF  POTENTIALS  AND  SIZES. 


KATIO 
OF  POTENTIALS, 

E.:3* 

VALUE  OF  EXPONENT,  X, 
FOB  KATIO  OP  LINEAR  DIMENSIONS,  m  = 

1  to  2 

3  to  8 

8  and  over. 

Uptoi 
tto4 
10  and  over 

3.00 
2.80 
2.60 

2.85 
2.70 
2.55 

2.70 
2.60 
2.50 

4J  DYNAMO-ELECTRIC  MACHINES.  [§  111 

The  values  given  in  the  above  table,  besides  for  the  com- 
parison of  machines  of  the  same  type,  are  found  to  hold  good 
also  for  the  comparison  of  the  outputs  of  similar  armatures 
in  frames  of  different  types.  But  the  figures  contained  in 
Table  XCVIII.  are  based  upon  the  assumption  that  the  field- 
.densities  and  the  conductor-velocities  of  the  two  machines  to 
be  compared  are  identical,  a  condition  which  is  very  seldom 
fulfilled  in  practice,  particularly  not  in  dynamos  of  different 
type,  as,  for  instance,  when  comparing  a  bipolar  with  a  multi- 
polar  machine.  Hence,  any  difference  in  the  field-densities 
and  in  the  peripheral  speeds  of  the  two  machines  to  be  com- 
pared must  be  properly  considered,  that  is  to  say,  the  expo- 
nent x  given  in  the  preceding  table  for  the  voltage-ratio  and 
the  size-ratio  in  question  must  be  multiplied  by  the  ratio  of 
their  products  of  field-density  and  conductor-velocity,  for,  the 
E.  M.  F.,  and  therefore  the  output,  of  a  dynamo  is  directly 
proportional  to  the  flux-density  of  its  magnetic  field  and  to 
the  cutting-speed  of  its  armature  conductors. 


CHAPTER  XXV. 

CALCULATION    OF    ELECTRIC    MOTORS. 

112.    Application   of    Generator    Formulae   to    Motor 
Calculation. 

All  the  formulae  previously  given  for  generators  apply 
equally  well  to  the  case  of  an  electric  motor;  for,  in  general,  a 
well-designed  generator  will  also  be  a  good  motor.  Hence 
the  first  step  in  calculating  an  electric  motor  is  to  determine 
the  electrical  capacity  and  E.  M.  F.  of  this  motor  when  driven 
as  a  generator,  at  the  specified  speed. 1 

Considering  a  given  dynamo  as  a  generator,  its  output,  Pl , 
in  watts,  at  the  terminals,  is  the  total  energy,  P't  generated  in 
its  armature  by  electromagnetic  induction,  diminished  by  the 
amount  of  energy  absorbed  between  the  armature  conductors 
and  the  machine  terminals;  that  is,  by  the  loss  due  to  inter- 
nal electrical  resistances.  In  other  words,  the  output  is  the 
total  electrical  energy  produced  in  the  armature  multiplied  by 
the  electrical  efficiency  of  the  dynamo.  The  output,  P\,  of 
the  same  machine,  when  run  with  the  same  speed  as  a  motor, 
is  the  useful  electrical  energy,  P',  active  within  its  armature  in 
setting  up  electromagnetic  induction,  less  the  energy  lost 
between  armature  and  pulley;  that  is,  less  the  loss  caused  by 
hysteresis,  eddy  currents,  and  friction,  or  is  the  product  of 
electrical  activity  and  gross  efficiency.  Conversely,  the  power, 
P" \  ,  to  be  supplied  to  the  generator  pulley,  must  be  the  total 
energy,  P't  produced  in  the  armature,  increased  by  an  amount 
equal  to  the  magnetic  and  frictional  losses,  or  must  be  P' 
divided  by  the  gross  efficiency.  And  the  energy,  P9,  finally, 
required  at  the  motor  terminals  in  order  to  set  up  in  the  arma- 
ture an  electrical  activity  of  P'  watts,  is  found  by  adding  to 
P'  the  energy  needed  to  overcome  the  internal  resistances  of 


"Calculation  of  Electric  Motors,"  by  Alfred  E.  Wiener,  Electrical  World, 
vol.  xxviii.,  pp.  693  and  725  (December  5  and  12,  1896). 

419 


420  DYNAMO-ELECTRIC  MACHINES.  [§  112 

the  motor,  or  by  dividing  P'  by  the  electrical  efficiency.  Des- 
ignating the  electrical  efficiency  of  the  machine,  /.  e.,  the  ratio 
of  its  useful  to  the  total  electrical  energy  in  its  armature,  by 
?;e,  and  its  gross  efficiency,  or  efficiency  of  conversion,  /.  e., 
the  ratio  between  the  electrical  activity  in  the  armature  and 
the  mechanical  power  at  the  pulley,  by  r/g,  we  therefore 
have: 

Output  of  machine  as  generator: 

Pi  =  r?exP';  .............  (378) 

Output  of  machine  as  motor: 

J>\  =  %Xf;  .........  .....(379) 

Power   to   be   supplied   to  machine  when  run  as  generator 
(driving  power): 


Energy  to  be  supplied  to  machine  when  run  as  motor  (intake 
of  motor)  : 

-P.  =  -f.     ..............  (881).. 

Ve 

Where  Plf    P9  =  electrical  energy  at  terminals  of  machine,  as 

generator  and  motor,  respectively; 
P'  —  electric  energy  active  in  armature  conduc- 

tors, being  the  same  in  both  cases; 
P"it  P\  —  mechanical    energy   at   dynamo    pulley,    for 

generator  and  motor,  respectively. 

By   transposition    of   (379)    the    electrical    capacity   of   the 
machine  can  be  expressed  by  the  motor  output,  thus: 


which  is  to  say  that,  in  order  to  find  the  dimensions  and  wind- 
ings for  a  motor  of 

P" 

hp  —  —  ^  horse-power, 

it  is  necessary  to  figure  a  generator  which  at  the  given  speed 
has  a  total  capacity  of 

p,=   :fl  =  74*  *»  watts 


§112]  CALCULATION  OF  ELECTRIC.  MOTORS.  421 

The  E.  M.  F.  for  which  the  generator  is  to  be  calculated,  or 
the  Counter  E.  M.  F.  of  the  motor,  is  the  voltage  at  the  motor 
terminals  diminished  by  the  drop  of  potential  within  the 
machine,  or: 

E'  =  E  -  I  X  (r'a  +  r'J  ,      (383) 

in  which  E    =   E.  M.  F.  active  in  armature,  in  volts; 
E     =  voltage  supplied  to  motor  terminals; 
/     =  current  intensity  at  motor  terminals; 
r'a   =  armature  resistance,  at  working  temperature, 

in  ohms; 
r'se  =  resistance  of  series  field,   warm,  in   ohms,  for 

series  and   compound  machines;  in  case  of 

shunt  dynamo  r'se  =  o. 

Formula  (383),  though  theoretically  accurate,  is  not  prac- 
tically so,  since  for  the  same  excitation,  armature  current  and 
speed,  the  counter  E.  M.  F.  of  a  motor  is  greater  than  the 
E.  M.  F.  when  used  as  a  generator,  for  the  following  reason: 
While  in  a  generator  a  forward  displacement,  or  a  lead,  of  the 
brushes  has  the  effect  of  weakening,  and  a  backward  displace- 
ment, or  a  lag,  that  of  strengthening  the  field  magnet,  in  a  motor 
a  lead  tends  to  magnetize,  and  a  lag  to  demagnetize  the  field. 
Sparkless  running,  however,  requires  a  lead  of  the  brushes  in 
a  generator  and  a  lag  of  the  same  in  a  motor,  so  that  in  both 
cases  the  armature  reactions  weaken  the  field.  Since  hysteresis 
as  well  as  eddy  currents  have  the  effect  of  shifting  the  magnetic 
field  in  the  direction  of  the  rotation,  thereby  increasing  the 
lead  in  a  generator  and  diminishing  the  lag  in  a  motor,  it 
follows  that — for  equal  magnetizing  force,  equal  current  inten- 
sity, and  equal  speed— the  lag  in  a  motor  is  less  than  the  lead 
in  a  corresponding  generator.  For  the  purpose  at  hand, 
however,  formula  (383)  gives  the  required  counter  E.  M.  F. 
with  sufficient  accuracy,  particularly  because  neither  the  cur- 
rent strength  nor  the  resistances  usually  being  prescribed,  the 
drop  must  be  estimated  by  means  of  Table  VIII.,  §  19. 

By  dividing  the  electrical  activity,  P',  as  obtained  from 
formula  (382),  by  the  E.  M.  F.,  E ',  the  current-capacity  of  the 
corresponding  generator  is  found: 

f  =       (384) 


422 


DYNAMO-ELECTRIC  MACHINES. 


[§112 


For  the  purpose  of  simplifying  this  conversion  of  a  motor 
into  a  generator  of  equal  electrical  activity,  the  following 
Table  XCIX.  is  given,  which  contains  the  average  efficiencies, 
and  the  active  energy  for  motors  of  various  sizes: 

TABLE  XCIX. — AVERAGE  EFFICIENCIES  AND  ELECTRICAL  ACTIVITY  OF 
ELECTRIC  MOTORS  OF  VARIOUS  SIZES. 


ELECTRICAL 

OUTPUT 

ACTIVITY 

OP  MOTOR 

ELECTRICAL 

GROSS 

COMMERCIAL 

IN  ARMATURE, 

IN 

EFFICIENCY. 

EFFICIENCY  . 

EFFICIENCY. 

IN  KILOWATTS. 

HORSE-POWER. 

hp 

*7e 

^ 

%  —  %  X  Vg 

p,       .  746  x  hp 

% 

\ 

.75 

.80 

.60 

.5 

1 

.82 

.82 

.67 

.9 

2 

.85 

.84 

.72 

1.8 

5 

.87 

.86 

.75 

4.0 

10 

.89 

.88 

.78 

8.5 

15 

.90 

.89 

.80 

12.6 

20 

.91 

.90 

.82 

16.6 

25 

.92 

.91 

.84 

20.5 

30 

.93 

.92 

.86 

24.5 

40 

.94 

.93 

.87 

32 

50 

.945 

.935 

.88 

40 

75 

.95 

.94 

.89 

60 

100 

.955 

.9425 

.90 

80 

150 

.96 

.945 

.91 

118 

200 

.97 

.9475 

.92 

158 

300 

.98 

.95 

.93 

236 

400 

.9825 

.9525 

.935 

318 

500 

.      .985 

.955 

.94 

391 

750 

.9875 

.9575 

.945 

585 

1000 

.99 

.96 

.95 

777 

If  a  dynamo  which  has  been  connected  for  working  as  a  gen- 
erator is  supplied  with  current  from  the  mains  instead,  it  will 
run  as  a  motor,  the  direction  of  rotation  depending  upon  the  man- 
ner of  field  excitation.  A  series  dynamo,  since  both  the  arma- 
ture and  field  currents  are  then  reversed,  will  run  in  the 
opposite  direction  from  that  which  it  was  driven  as  generator, 
and  must  therefore  -have  its  brushes  reversed  and  given  a  lead 
in  the  opposite  direction;  or,  if  direction  in  the  original  gen- 
erator direction  is  desired,  must  have  either  its  armature  or 
its  field  connections  reversed.  A  shunt  dynamo  will  turn  in 
the  same  direction  when  run  as  a  motor,  for,  while  the  armature 


§113]  CALCULATION  OF  ELECTRIC  MOTORS.  423 

current  is  reversed,  the  exciting  current  will  have  the  same 
direction  as  when  worked  as  a  generator.  A  compound  dynamo, 
finally,  will  run  as  a  motor  in  the  opposite  direction,  if  the  series 
winding  is  more  powerful  than  the  shunt,  and  in  the  same  sense, 
if  the  shunt  is  the  more  powerful;  and  while  the  field  excitation 
as  a  generator  is  the  sum  of  the  series  and  shunt  windings  as  a 
motor  it  is  their  difference. 

113.  Counter  E.  M.  F. 

Whereas  in  a  generator  there  is  but  one  E.  M.  F. ,  in  a 
motor  there  must  always  be  two.  If  /  =  current  at  machine 
terminals,  E  =  direct  E.  M.  F.,  E  —  counter  E.  M.  F., 
R  =  total  resistance  of  circuit,  and  r  =  internal  resistance  of 
machine,  this  difference  between  a  generator  and  a  motor  can 
be  best  expressed  1  by  the  formulae  for  the  current  in  the  two 
cases,  thus — 

for  generator:  _  E 

=  R  ; 

for  motor:  E  -  E  __,,         _,        _ 

7=7  -  ,   or  E  —  E  —  Ir. 

r 

The  current  and  direct  E.  M.  F.  are  the  same  in  both  cases, 
but  the  resistance  is  much  less  in  case  of  a  motor,  the  differ- 
ence being  replaced  by  the  counter  E.  M.  F.,  which  acts  like  a 
resistance  to  reduce  the  current. 

Upon  the  amount  of  this  counter  E.  M.  F.  depend  the 
speed  and  the  current,  and  therefore  the  power  of  an  electric 
motor.  For,  since  the  E.  M.  F.  generated  by  electromagnetic 
induction  is  proportional  to  the  peripheral  velocity  of  the 
armature,  it  follows  that,  other  factors  remaining  unchanged, 
the  speed  conversely  depends  upon  the  counter  E.  M.  F.  only. 
The  latter  is  the  case  in  a  series  motor  run  from  constant  cur- 
rent supply,  since  in  this  the  magnetizing  force  is  constant  at 
all  loads.  In  a  shunt  motor,  however,  the  field  current  varies 
with  the  load,  and  the  speed,  therefore,  depends  upon  the  field 
magnetism  as  well  as  upon  the  counter  E.  M.  F.  If  the 
exciting  current  in  a  constant  potential  shunt  motor  is  de- 
creased, the  E.  M.  F.  decreases  correspondingly,  and  a  rise  of 


1  "The  Electric  Motor,"  by  Francis  B.  Crocker,  Electrical  World,  vol.  xxiii. 
p.  673  (May  19,  1894). 


424  D  YNAMO-ELECTRIC  MA  CHINES.  [§  1  14 

the  current  flowing  in  the  motor  is  the  consequence,  as  fol- 
lows directly  from  the  above  equation  for  the  motor  current. 
The  speed  in  this  case,  therefore,  rises  until  the  counter 
E.  M.  F.  reaches  a  sufficient  value  to  shut  off  the  excess  of 
current. 

If  the  counter  E.  M.  F.  is  low,  which  is  the  case  when  the 
motor  is  starting  or  running  slowly,  resistance  has  to  take  its 
place  in  order  to  govern  the  current  of  the  motor.  The  intro- 
duction of  resistance  in  series  with  the  armature,  the  so-called 
starting  resistance,  is  usually  resorted  to  for  this  regulation,  but 
this  is  very  wasteful  of  energy  and  involves  the  use  of  a  large 
and  clumsy  rheostat,  while  the  counter  E.  M.  F.  itself  affords 
a  means  to  easily  design  a  motor  to  run  at  the  same,  or  at  a 
higher,  speed  at  full  load  than  when  lightly  loaded.  This  may 
be  done  by  slightly  exaggerating  the  effect  of  armature  reac- 
tion, so  that  the  field  magnetism  will  be  considerably  reduced 
by  the  large  armature  current  which  flows  at  full  load,  thus 
diminishing  the  counter  E.  M.  F.  and  increasing  the  speed  in 
the  manner  explained  above.  In  this  way  the  remarkable  effect 
of  greater  speed  with  heavier  load  is  obtained  without  any 
special  device  or  construction;  all  that  is  necessary  being  a 
slight  modification  in  design,  involving  no  increase  in  cost  or 
complication. 

114:.  Speed  Calculation  of  Electric  Motors. 

If  a  generator,  which  at  a  speed  of  Nl  revolutions  per 
minute  produces  a  total  E.  M.  F.  of 

E\  =  E  +  fy.  (r;+  revolts, 

is  run  as  a  motor  having  same  current  strength  in  armature, 
the  motor  armature,  in  order  that  no  more  nor  less  than  this 
current,  /',  its  full  load  as  a  generator,  shall  flow,  must  gen- 
erate a  counter  E.  M.  F.  of 

E\  =  E  I  X  (/•'.  +  ry  volts. 

The  speed  necessary  to  generate  this  back  voltage,  speed  being 
proportional  to  voltage,  is: 


X 


§  114]  CALCULATION  OF  ELECTRIC  MOTORS.  425 

which  is  the  speed  of  the  motor  at  full  load,  provided-  the 
E.  M.  F.,  £,  supplied  to  its  terminals  is  equal  to  the  voltage 
when  run  as  generator. 

The  speed  of  the  motor  for  any  given  E.  M.  F.,  applied  to 
its  armature  terminals,  depends  (i)  upon  the  load  impressed 
upon  the  motor  armature,  or  the  torque  r,  it  has  to  exert; 
(2)  on  the  electrical  resistance  (r'&  -j-  r'se),  of  the  armature  and 
the  series  field;  and  (3)  upon  its  specific  generating  power,  or 
its  capability  of  producing  counter  E.  M.  F.  ;  /.  £.,  the  number 
of  volts,  /,  it  produces  at  a  speed  of  one  revolution  per 
second. 

The  specific  generating  power  of  the  motor  being 

j\r 

e"  =  <P  x  —  T-  X  io~8  volts  at  i  rev.  per  sec.  ,     (386) 
«p 

where  $     =  useful  flux,  in  webers; 

JVG  —  number  of  conductors  on  armature; 

;;'p  —  number  of  pairs  of  armature  circuits  electrically 

in  parallel; 

the  total  counter  E.  M.  F.  at  the  required  speed  of  N^  revolu- 
tions per  minute,  will  be 

£<  .  -  e.  x  ^  _  g  x  jye  x  N; 

**-          <  fo    -  60  X   10"  X  «•„  ..... 

and  the  current  flowing  in  the  armature,  therefore,  is: 


(388) 


r\  +   r'se 

The  activity  of  this  current  expended  upon  the  counter 
E.  M.  F.  will  be  their  product,  E\  x  /'  watts,  and  this  must 
be  equal  to  the  total  rate  of  working,  which  is  the  product  of 
circumferential  speed  and  turning  moment,  or  torque;  that  is, 
it  must  be  equal  to 

2  7t  X  N^  X  r  x    — — •  watts , 
33,000 

where  the  torque,   r,  is  calculated  from   formula  (93),    §  40; 
hence  we  have : 

F        "       N* 

60  JV  746 

X   —     -=  27rx-7-2XrX- 

r*  +  rse  60  550  ' 


DYNAMO-ELECTRIC  MACHINES.  [§  114 

from  which 

'          Nt  =  60  X   (*   -  8.5*  X    <r*+£*J-\     (389, 

From  (389)  follows  that,  if  either  the  internal  resistance  or 
the  torque  is  zero,  since  the  second  term  in  the  parenthesis 
then  disappears,  the  speed  of  the  motor  is: 


..(390) 


This  reduced  formula  (390),  indeed,  holds  very  nearly  in 
practice  for  very  large  motors  (in  which  the  internal  resistance 
is  very  small),  and  also  is  approximately  followed  in  case  of 
motors  running  free  (the  torque  then  being  only  that  necessary 
to  overcome  the  frictions). 

The  important  requirement  of  constant  speed  under  variable 
load  may  be  almost  perfectly  met  by  the  compound-wound 
motor,  is  nearly  met  by  the  shunt-wound  motor,  and  is  not 
met  without  the  aid  of  special  mechanism  by  the  series-wound 
motor.  A  compound-wound  motor  will  maintain  its  speed 
perfectly  constant  under  all  loads,  if  the  series  winding  is  so 
adjusted  that  the  increase  of  current  strength  through  the 
series  coils  and  armature  shall  diminish  the  M.  M.  F.  of  the 
field  magnets  to  the  degree  necessary  to  compensate  for 
the  drop  of  pressure  in  the  armature  winding.  (See  §  148.) 

If  constant  speed  is  required,  such  as  is  the  case  in  operating 
silk  mills  and  textile  machinery,  the  compound  motor  will 
therefore  be  found  to  give  the  best  satisfaction,  since  in  shunt 
motors,  although  running  with  ''practically  constant"  speed, 
the  variation  may  be  too  great  to  be  without  influence  upon  the 
product  of  manufacture. 

When  started  without  load  the  speed  of  a  shunt  motor  grad- 
ually increases  and  reaches  a  maximum,  from  which  it  falls 
down  again  as  soon  as  the  load  is  put  on.  The  rise  at  no  load 
is  due  to  the  fact  that  since  the  potential  at  the  field  terminals 
is  constant,  the  field  current  decreases  as  the  resistance  of  the 
field  coils  increases,  owing  to  their  heating,  thereby  decreasing 
the  magnetizing  power,  and  in  consequence  the  counter 
E.  M.  F.  of  the  motor.  The  subsequent  decrease  of  the  speed 
is  caused  by  the  increase  of  the  armature  current  with  increas- 


§115] 


CALCULATION  OF  ELECTRIC  MOTORS. 


427 


ing  load,  and  by  the  heating  of  the  armature  due  to  the  passing 
current,  the  counter  E.  M.  F.  decreasing  with  increasing  Brop 
of  voltage  in  the  armature.  Tests  made  by  Thomas  J.  Fay  ' 
with  shunt  motors  of  various  sizes  gave  the  results  compiled  in 
the  following  Table  C.  : 

TABLE  C. — TESTS  ON  SPEED- VARIATION  OF  SHUNT  MOTORS. 


Normal 

: 

CAPACITY 

Speed, 
at 
No  Load, 

Increase  of  Speed 
from  No  Load,  Cold, 
to  No  Load,  Hot, 

Decrease  of  Speed 
from  No  Load,  Hot, 
to  Full  Load,  Hot, 

Final  Change 
in  Speed. 

MOTOR, 

Cold, 
Revs,  per 

Due  to  Heating  of 
Field  Coils. 

Due  to  Heating 
of  Armature. 

-f-  =  Increase. 
—  =  Decrease. 

HP. 

Mm 

3 

1400 

20  £  of  normal  speed 

12  %  of  normal  speed 

-f  8  %  of  normal  speed. 

5 

1200 

8V4                      '* 

5 

-4—  3V^»            *             <fc 

7^ 

1360 

5/4                    " 

4              •'            » 

-I-  \\fa            '             " 

10 

1200 

2                            " 

8%          **            ' 

gajC             <             «t 

15 

1180 

2^ 

3/^          "           ' 

-1 

20 

860 

% 

4 

-3^ 

From  this  table  it  will  be  seen  that  the  resistance  of  the  field 
and  of  the  armature  can  be  so  proportioned  with  relation  to 
each  other  that  the  final  speed  at  full  load  hot  is  equal  to  the 
normal  speed  at  no  load  cold.  But  in  order  to  reduce  to  a 
minimum  the  variation  of  the  speed  during  the  period  of  heat- 
ing up  of  the  motor,  it  is  necessary  that  both  the  increase  due 
to  the  heating  of  the  magnet  coils  and  the  decrease  due  to  the 
heating  of  the  armature  should  be  reduced  as  much  as  possible. 
For  this  purpose  the  field  winding  should  be  so  proportioned 
as  not  to  heat  very  much  above  the  temperature  of  the  sur- 
rounding air,  and  the  armature  resistance  should  be  as  low  as 
possible. 

115.  Calculation  of  Current  for  Electric  Motors. 

a.    Current  for  Any  Given  Load. 

The  current  in  the  armature  of  a  motor  for  any  load,  P"K 
watts  =  746  x  hp,,.  horse  power,  at  the  pulley,  since  at  any  in- 
stant the  entire  energy  supplied  to  the  motor  must  be  equal  to 
the  sum  of  the  expenditures,  can  be  found  from  the  equation: 

E  X  (/'x  +  /8h)  -  P\  +  /V  X  (/a  +  r^)  +  E  X  /8h  -f  P9, 


1  "  Constant  Speed  Motors,"  by  Thomas  J.  Fay,  Electrical  Age,  vol.  xv.  p. 
38  (January  19,  1895). 


428  DYNAMO-ELECTRIC  MACHINES.  [§  115 

which  gives: 


_  E-      J5*-4  (r'a  +  r'se)  X 
~~ 


where  E  =  line  potential    supplied    to    motor   terminals,    in 

volts; 
/'x  —  current  in  armature  of  motor,  in  amperes,  for  any 

given  load  ; 

/8h  =  current  in  shunt  field  of  motor,  in  amperes; 
Pffx  =  useful  load  of  motor,  in  watts; 
P0  =  energy  required  for  no  load,  in  watts; 
r'&  —  armature  resistance,  in  ohm; 
r'se  =  series  field  resistance,  in  ohm. 

Formula  (391)  directly  applies  to  series-  and  compound- 
wound  motors;  in  case  of  shunt-wound  motors,  r'K  being  =  o, 
it  reduces  it  to: 


--&  0 

2^'a 

b.    Current  for  Maximum   Commercial  and  Electrical 
Efficiency.  ' 

As  the  energy  commercially  utilized  in  a  motor  is: 
P\  =  E  X  /'  -  r  X  (r'a  +  r'se)  -  P0 
and  the  entire  energy  supplied  is: 

f,  =  E  x  /'  +  P+  ; 
the  commercial  efficiency  can  be  expressed  by 


_ 


and  similarly  the  electrical  efficiency,  by: 

^e  ~  ~~~     E  I1  4-  P* 
P8h  being  the  energy  absorbed  in  the  shunt. 


'  "  Shunt  Motors,"  by  W.   D.  Weaver,  Electrical  World,  vol.  xxi.  p.    137 
(February  25,  1893). 


§116]  CALCULATION  OF  ELECTRIC  MOTORS.  429 

These  efficiencies  are  maxima  for: 


jr i    /     —   sn     i      -    o     i      i   —  BLI  i  §       ah 


and 


-  (i) 


respectively.  Formula  (393),  therefore,  gives  the  current  that 
must  be  supplied  to  the  armature  of  a  motor  in  order  to  have 
the  maximum  commercial  efficiency,  and  formula  (394)  the 
current  for  maximum  electrical  efficiency. 

116.  Designing  of  Motors  for  Different  Purposes. 

According  to  the  purpose  a  motor  has  to  serve,  its  efficiency 
is  desired  to  either  be  high  and  nearly  constant  over  a  wide 
range  of  its  load,  or  to  increase  in  proportion  with  the  output 
and  be  highest  at  the  maximal  load  the  motor  can  carry. 

The  shape  of  the  efficiency  curve  of  a  motor  depends  upon 
the  proportioning  of  its  various  losses.  The  losses  in  a  motor 
are  of  two  kinds,  fixed  and  variable.  The  fixed  losses  are 
those  due  to  the  shunt  field  current,  hysteresis,  and  eddy  cur- 
rents, brush  friction,  bearing  friction,  and  air  resistance.  The 
variable  losses  are  those  due  to  armature  and  series  resistance, 
and  to  commutation,  and  increase  with  the  load.  If  the  fixed 
losses  are  small  compared  with  the  variable  ones,  the  efficiency 
at  light  loads  will  be  high  and  will  rapidly  drop  as  the  load,  and 
with  it  the  variable  loss,  increases.  If,  on  the  other  hand,  the 
fixed  losses  are  very  large,  and  the  variable  losses  small,  the 
efficiency  with  small  loads  will  be  low,  but  will  increase  as 
the  load  becomes  greater,  for  the  reason  that  the  total  energy 
increases  proportional  to  the  load  while  the  losses  in  this  case 
remain  nearly  constant,  increasing  but  very  little  with  the  load. 

In  order  to  have  the  fixed  losses  in  a  motor  small  and  the 
variable  losses  great,  it  is  necessary  to  employ  a  massive  mag- 
netic circuit  with  few  shunt  ampere-turns,  an  ample  cross-sec- 
tion of  iron  in  the  armature  core,  and  a  large  number  of  turns 
on  armature  and  series  field;  hence  the  energy  lost  in  shunt 
field  excitation,  in  hysteresis,  and  eddy  currents  is  small,  but 
that  lost  by  armature  and  series  field  resistance  and  by  com- 


430 


DYNAMO-ELECTRIC  MACHINES. 


[§  H6 


mutation  is  great.     The  reverse  of  these  conditions  insures  an 
increase  in  the  fixed,  or  a  decrease  in  the  variable,  losses. 

Curves  I.  and  II.,  Fig.  315,  show  the  variation  of  the  com- 
mercial efficiency  with  the  load  in  two  motors  of  different  de- 
sign, both  having  the  same  efficiency,  rfe  =  So  per  cent,  at 


100  # 


1A         H        H         i 
Fig.  SIS-— Efficiency  Curves  of  Two  Motors  of  Different  Design. 

normal  load,  but  I.  having  very  high  efficiencies  at  light  loads, 
while  II.  has  very  low  efficiencies  at  small  loads,  but  even 
greater  than  normal  efficiency  with  overloads: 

TABLE  CL— COMPARISON  OP  EFFICIENCIES  OF  Two  MOTORS  BUILT 
FOR  DIFFERENT  PURPOSES. 


EFFICIENCY  AT  VARIOUS  LOADS. 


^  Load. 

^  Load. 

H  Load. 

Normal 
Load. 

25  Per  cent. 
Overload. 

50  Per  cent. 
Overload. 

Per  cent. 

Per  cent. 

Per  cent. 

Per  cent. 

Per  cent. 

Per  cent. 

I. 

70 

80 

83 

80 

73 

65 

II. 

40 

60 

72 

80 

86 

90 

An  efficiency  curve  similar  to  I.  is  desired  in  constant  power 
work  where  the  greatest  load  is  put  on  the  motor  but  once  in 
starting,  and  where,  after  the  friction  of  rest  has  been  over- 
come, the  motor  is  called  upon  to  work  on  half  to  three-fourths 
its  normal  output  continually;  motors,  consequently,  which 
are  to  be  employed  for  running  printing  presses,  machine- 


§117]  CALCULATION  OF  ELECTRIC  MOTORS.  43  * 

shop  tools,  power  pumps,  etc.,  must  be  designed  with  a  heavy 
frame  of  low  magnetic  density,  a  weak  field,  small  excitation, 
and  a  powerful  armature.  In  order  to  obtain  an  efficiency 
curve  similar  to  II.,  which  is  preferable  in  all  cases  where  the 
motor  is  not  doing  steady  work,  but  is  called  upon  to  give 
more  than  its  normal  power  at  frequent  intervals,  as,  for  in- 
stance, in  operating  electric  railways,  elevators,  cranes,  hoists, 
etc.,  the  motor  must  be  provided  with  a  light  frame  of  high 
magnetic  density,  a  strong  field,  powerful  excitation,  and  a 
weak  armature. 

117.    Railway  Motors. 

a.   RAILWAY  MOTOR  CONSTRUCTION.  ' 

The  construction  of  motors  used  for  railway  propulsio.n 
deviates  in  many  respects,  electrically  as  well  as  mechanically, 
from  that  of  ordinary  motors.  The  principal  conditions  that 
must  be  fulfilled  in  the  design  of  a  railway  motor  are  the  fol- 
lowing: 

(1)  The  motor  should  be  extremely  compact,  so  that  it  may 
be  easily  placed  in  the  space  available  within  the  truck;  yet  it 
must  be  easily  accessible,  and  all  its  parts  subject  to  wear 
must  be  easily  exchangeable.     All  parts  of  the  machine  must 
furthermore  be  so  designed  and  the  winding  so  executed  that 
the  continual  vibrations  due  to  the  motion  of  the  car  are  un- 
able to  loosen  the  same,  or  to  get  them  out  of  working  order, 

(2)  A  railway  motor  must  be  so  designed  that  with  minimum 
weight  a  maximum  output  is  obtained. 

(3)  The  speed  of  the  armature  must  be  properly  chosen  with 
regard  to  the  minimum  and  maximum  load,  to  the  speed  of 
the  car,  the  diameter  of  the  car  wheels,  and  the  ratio  of  speed 
reduction. 

(4)  The  regulation  of  the  speed  should  be  simple,  reliable, 
and  perfectly  adapted  to  all  grades  and  curvatures  of  the  track. 

(5)  The  type  of  the  motor  should  be  so  chosen,  and  the  de- 
sign so  carried  out,  that  there  is  no  external  magnetic  leakage, 


1  See  "  Praktische  Gesichtspunkte  flir  die  Konstruction  von  Motoren  fiir 
Strassenbahnbetrieb,"  by  Emil  Kolben,  Elektrotechn.  Zeitschrift,  vol.  xiii.  No. 
34  and  35  (August  19  and  26,  1892). 


432  DYNAMO-ELECTRIC  MACHINES.  [§  117 

that  at  the  same  time  all  the  vital  parts  of  the  motor  are  pro- 
tected from  mechanical  injuries,  and  that  it  can  be  so  sup- 
ported from  the  truck  that,  if  possible,  none  of  its  weight  is 
resting  directly  upon  the  car  axle.  Particular  care  must  also 
be  bestowed  upon  the  selection  of  insulating  materials  and  the 
manner  of  insulation,  in  order  to  guard  the  machine  against 
the  influence  of  dampness,  mud,  and  water. 

(i)    Compact  Design  and  Accessibility. 

Since  it  is  usual  to  equip  each  car  with  two  motors  which 
are  directly  suspended  from  the  car  axles  and  the  frame  of  the 
truck,  the  extreme  dimensions  of  the  motor  are  limited  by  the 
diameter  of  the  wheels,  their  distance  apart  longitudinally, 
and  by  the  gauge  of  the  track.  The  trucks  most  commonly 
used  have  30  or  33-inch  wheels,  a  wheel  base  of  6  to  7  feet, 
and  the  standard  gauge  of  4  feet  8£  inches.  The  height  of 
the  motor  is  further  limited  by  the  condition  that  a  space  of  at 
least  3  inches  should  be  left  between  the  lowest  point  of  the 
motor  and  the  top  of  the  rails  in  order  to  enable  the  motor  to 
pass  over  stones  or  other  small  obstructions  upon  the  track. 
The  arrangement  should  be  such  that  the  working  parts  can 
be  easily  inspected  during  the  trip  from  a  trapdoor  in  the 
flooring  of  the  car.  If  it  is  impracticable  to  provide  the  car- 
barn with  pits  below  the  tracks,  the  motor  should  be  so 
arranged  that  the  armature,  the  field  coils,  and  the  brushes 
can  be  taken  out  through  the  same  trapdoor.  In  order  to 
facilitate  the  quick  replacing  of  a  disabled  armature,  it  is  ad- 
visable to  split  the  motor  frame  horizontally,  and  to  make  one 
part  revolvable  by  means  of  strong  hinges. 

(2)  Maximum  Output  with  Minimum   Weight. 

The  energy  required  for  propelling  a  car  being  proportional 
to  its  weight,  it  must  be  the  aim  to  make  the  entire  equipment 
as  light  as  is  consistent  with  strength  and  durability.  In  order 
to  reduce  the  weight  of  the  motor  to  a  minimum,  it  is  of  the 
utmost  importance  to  use  only  the  best  materials  suitable  for 
the  respective  parts,  namely,  the  softest  annealed  sheet  iron 
for  the  armature  core,  silicon  bronze  or  drop-forged  copper 


§117]  CALCULATION  OF  ELECTRIC  MOTORS.  433 

for  the  commutator  segments,  and  softest  cast  steel  for  the 
field  frame.  If  reduction  gears  are  used,  the  pinions-should 
be  of  hard  bronze  or  of  good  tool  steel,  and  the  gear  wheels 
of  cast  steel,  or  of  fine  grain  cast-iron.  In  order  to  obtain 
the  maximum  possible  output,  the  magnetic  circuit  of  the 
motor  should  have  as  small  a  reluctance  as  possible,  and  the 
magnetic  leakage  should  likewise  be  reduced  as  much  as  pos- 
sible. The  former  is  attained  by  the  use  of  toothed  or  perfor- 
ated armatures  with  very  small  air  gaps;  and  the  latter  by 
proper  selection  of  the  type.  The  armature  should  be  made 
most  effective  by  providing  it  with  a  great  number  of  turns; 
the  sparking  which  would  thus  result  under  ordinary  condi- 
tions being  checked  by  the  use  of  carbon  brushes  which  are  set 
radially  in  order  to  enable  reversibility  in  the  direction  of  rota- 
tion of  the  motor.  The  weight  efficiency  of  various  railway 
motors  is  given  in  Table  CIL,  p.  435. 

(3)  Speed^  and  Reduction  Gearing. 

The  speed  of  the  motor  naturally  depends  upon  the  car 
velocity  desired,  upon  the  size  of  the  car  wheels,  and  upon  the 
method  used  for  the  mechanical  transmission  of  the  motion 
from  the  armature-shaft  to  the  car  axle.  The  maximum  speed 
of  the  car,  according  to  local  conditions  (size  of  town,  amount 
of  traffic  in  streets,  etc.)  varies  from  8  to  15  miles  per  hour, 
the  greatest  speed  of  the  car  axle,  therefore,  provided  that  30- 
inch  wheels  are  used  with  the  slow,  and  33-inch  wheels  with 
the  fast  running  cars,  ranges  between  90  and  150  revolutions, 
respectively. 

The  methods  of  transmission  most  commonly  employed  in 
electric  railway  cars  are  the  double  and  single  spur  gearing, 
and  the  direct  coupling;  worm  gearing,  bevel  gearing,  link- 
chains,  and  crank-rods  being  used  only  in  single  cases.  The 
employment  of  double  spur  gearing  was  necessary  with  the  earlier 
railway  motors  which  were  run  at  from  1000  to  1200  revolu- 
tions per  minute,  and  which,  therefore,  had  to  have  their 
speed  reduced  in  the  ratio  of  from  10:  i  to  15:  i.  High-speed 
railway  motors,  however,  on  account  of  the  noise  and  wear 
connected  with  the  presence  of  four  gear  wheels  for  each 
motor,  that  is  eight  gears  per  car,  proved  too  inconvenient 


434  DYNAMO-ELECTRIC  MACHINES.  [§117 

and  too  expensive  to  maintain,  and  low-speed  motors  of  from 
400  to  500  revolutions  per  minute,  necessitating  but  a  single 
spur  gearing  with  a  reduction-ratio  of  from  4:1  to  5  :  i,  were 
next  resorted  to.  If  the  spur  gears  for  such  single  reduction 
motors  are  provided  with  broad  and  carefully  cut  teeth,  and  are 
run  in  oil,  both  noise  and  wear  are  very  small,  and  the  effi- 
ciency is  comparatively  high.  Worm  gearing  can  be  employed 
for  any  speed  ratio  within  the  limits  of  railway  motor  reduction, 
and  by  proper  design  very  high  efficiencies  may  be  attained. 
If  the  worm  is  carefully  cut  from  a  solid  piece  of  tool  steel, 
and  the  rim  of  the  worm  wheel  made  of  hard  phosphor  bronze, 
and  if  the  dimensions  are  so  chosen  that  an  initial  speed  of  20 
to  40  feet  per  second  is  obtained,  the  efficiency  when  run  in 
oil  may  reach  90  per  cent,  and  over. !  If  no  speed  reduction 
at  all  is  desired,  that  is  to  say,  if  the  motor  is  to  be  directly 
coupled  with  the  car  axle,  its  normal  speed  must  be  between 
100  and  150  revolutions  per  minute.  From  tests  made  by 
Professor  S.  H.  Short,2  the  saving  of  power  consumed  in 
operating  a  directly  coupled,  gearless  street  car  motor  is  found 
to  be  from  10  to  30  per  cent,  as  compared  with  double  spur 
gearing,  and  from  5  to  10  per  cent,  as  compared  with  single 
spur  gearing,  according  to  the  load. 

In  order  to  show  what  has  been  done  in  the  way  of  compact 
design  and  weight-efficiency  of  railway  motors  of  various  speed 
reductions,  the  following  Table  CII.  has  been  prepared,  giving 
the  specific  weight,  the  speed,  kind  and  ratio  of  reduction,  the 
type  and  dimensions  of  the  frame,  the  space-efficiency,  and  the 
size  of  the  armature,  of  the  most  common  railway  motors  in 
practical  use.  The  figures  given  for  the  dimensions  of  the 
field  frame  do  not  include  any  supporting  or  suspension 
brackets,  lugs,  or  other  extensions  that  may  be  attached  to,  or 
cast  in  one  with  the  frame,  but  relate  only  to  the  magnetic 
portion  of  the  field  casting.  This  is  done  to  bring  all  the 
space  efficiencies  to  a  common  basis,  thus  enabling  a  fair  com- 
parison of  the  various  types: 


1  See  "  Schneckengetriebe    in  Verbindung  mit   Elektromotoren,"  by  Emil 
Kolben,  Elektrotechn.  Zeitschr.^  vol.  xvi.  p.  514  (August  15,  1895). 

2  "  Gearless  Motors,"  by  Sidney  H.  Short,  Electrical  Engineer,  vol.  xiii.  p. 
386  (April  13,  1892)  ;  Electrical  World,  vol.  xix.  p.  263  (April  16,  1892). 


117]  CALCULATION  OF  ELECTRIC  MOTORS. 

fl-S 


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436  DYNAMO-ELECTRIC  MACHINES.  [§  117 

(4)   Speed  Regulation. 

In  order  to  effect  the  variation  of  the  speed  of  railway 
motors  within  wide  limits  it  is  desirable  that  their  field  mag- 
nets should  be  series  wound.  The  strength  of  the  magnetic 
field  can  then  be  regulated  either  by  inserting  resistance  into 
the  main  circuit,  in  connection  with  partial  short-circuiting  of 
the  field  coils,  or  by  altering  the  combination  of  the  magnet 
spools,  or  by  series-parallel  grouping  of  the  armatures  and 
field  coils  of  the  two  motors. 

In  the  Resistance  Method  the  insertion  of  rheostat-resistance 
into  the  main  circuit,  by  reducing  the  effective  E.  M.  F., 
causes  a  decrease  in  the  speed  of  the  motor;  in  this  case  the 
cross-section  of  the  magnet  wire  must  be  so  dimensioned  as  to 
carry  the  maximum  current,  but  the  number  of  turns  must  be 
chosen  far  greater  than  is  required  for  the  production  of  the 
requisite  number  of  ampere-turns  at  maximum  current  and 
maximum  speed.  For,  almost  the  full  field  strength  must  be 
obtained  with  a  comparatively  small  current-intensity,  and  it 
it  therefore  necessary  to  short-circuit  a  portion  of  the  magnet 
coils  at  maximum  load.  That  is  to  say,  in  order  to  raise  the 
torque  of  the  motor  for  increased  loads,  only  one  of  the  two 
factors  determining  the  same  is  increased,  namely  the  current 
strength  in  the  armature,  while  the  field  current  remains  the 
same.  In  order  to  do  this  without  excessive  sparking,  caused 
by  the  fact  that  the  brushes,  not  being  adjustable,  are  never 
at  the  neutral  'points  of  the  resultant  field,  carbon  brushes 
must  be  used,  whose  large  contact  resistance  considerably  re- 
duces the  current  in  the  coils  short-circuited  by  the  brushes. 

The  Combination  Method  of  speed  regulation  consists  in  suit- 
ably changing  the  grouping  of  the  magnet-spools.  For  this 
purpose  it  is  necessary  to  wind  the  magnet  coil  in  sections, 
equal  portions  of  which  are  placed  on  each  magnet,  and  to 
connect  the  terminals  of  these  sections,  usually  three  in  num- 
ber, to  a  switch,  or  controller,  of  proper  design.  At  the  max- 
imum load  of  the  motor  the  three  sections  are  connected  in 
parallel,  and  for  this  combination,  therefore,  the  cross-section 
of  the  winding  is  to  be  calculated.  For  starting  the  car  all 
sections  are  connected  in  series,  and,  if  no  precaution  were 
taken,  the  magnet  winding  would,  in  consequence,  have  to 


§  117]  CALCULATION  OF  ELECTRIC  MOTORS.  437 

carry  the  full  starting  current,  which  may  be  4  to  6  times  the 
maximum  normal  current.  In  order  to  avoid  overheating  and 
damage  due  to  this  starting  current,  a  starting  rheostat  must 
be  placed  in  circuit,  the  resistance  of  this  rheostat  being  so 
dimensioned  that  the  starting  current  is  brought  down  in 
strength  to  that  of  the  maximum  working  current. 

While  with  the  two  former  methods  of  speed  regulation  the 
two  motors  of  the  car  are  permanently  connected  in  parallel, 
in  the  Series- Parallel  Method  of  control,  finally,  both  the  arma- 
tures and  magnet-coils  of  the  two  motors  can  be  grouped  in 
any  desired  combination.  The  same  number  of  combinations 
is  therefore  possible  with  less  elements,  and  only  two  sections 
per  magnet-coil  are  necessitated.  Since  by  placing  both  arma- 
tures and  all  four  field-sections  in  series  the  starting  current 
is  considerably  reduced,  less  resistance  is  needed  in  the  start- 
ing rheostat,  and  a  saving  of  energy  is  effected  by  this  method. 
For  calculating  the  carrying  capacity  of  the  magnet-wire  the 
last  two  positions  of  the  series-parallel  controller  are  essential: 
for  maximum  speed  the  two  motors,  each  having  one  coil  cut 
out,  are  placed  in  parallel;  and  in  the  position  for  the  next 
lower  speed  both  motors  with  their  two  coils  in  series  are 
grouped  in  parallel. 

(5)  Selection  of  Type. 

The  most  important  consideration  in  the  selection  of  the 
type  for  a  railway  motor  is  the  condition  that  there  should  be 
no  external  magnetic  leakage,  as  otherwise  the  neighboring 
iron  parts  of  the  truck  may  seriously  influence  the  magnetic 
distribution,  and,  furthermore,  small  iron  objects,  such  as 
nails,  screws,  etc.,  may  be  attracted  into  the  gap-space  and 
may  injure  the  armature.  In  order  to  protect  the  motor  from 
dampness  and  mechanical  injuries,  such  types  are  to  be  .pre- 
ferred in  which  the  yoke  surrounds  the  armature,  and  which 
therefore  can  easily  be  so  arranged  that  the  frame  completely 
encases  all  parts  of  the  machine.  The  types  possessing  the 
latter  feature  are  the  iron-clad  types,  Figs.  203  to  207,  §72, 
and  Figs.  217  to  220,  §73,  the  radial  outerpole  type,  Fig.  208, 
and  the  axial  multipolar  type,  Fig.  212;  and  as  can  be  seen 
from  the  preceding  Table  CII.,  these  are  in  fact  the  forms  of 
machines  that  are  used  in  modern  railway  motor  design. 


438  DYNAMO-ELECTRIC  MACHINES.  [§117 

b.   CALCULATIONS  CONNECTED  WITH  RAILWAY  MOTOR  DESIGN.  J 

(i)   Counter  E.  M.  F.,  Current,  and  Energy  Output  of  Motor. 

Inserting  into  the  formula  for  the  counter  E.  M.  F., 

,,,       N,         N 
E  —  —^  X  -  -  X   #  X  io8, 
n\          60 

the  value  of  the  useful  flux  from  §§  86  and  87, 

4  n        AT 

^se    X   /  _       WBe  X  I 


(R  (R  10  (R'         ' 

-  X  (R 
4  n 

where  &      —   magnetomotive  force,  in  gilberts; 

A  T  •=.  JVS&  X  /  =  magnetizing  force,  in  ampere-turns; 
(R      =  reluctance  of  magnetic  circuit,  in  oersteds; 

10  10          i  /'' 

(R'     =-        x   &    =  -  -  X  -  -  X  -T^-  , 
47T  4^         p          Sm 

jj   =  permeability  of  magnet-frame,  at  normal 

load; 

l"m  —  length  of  magnetic  circuit,  in  inches; 
Sm  =  area  of  magnet-frame,  in  square  inches; 

we  obtain: 


If  the  internal  resistance  of  the  motor,  /.  e.,  armature  resist- 
ance plus  series  field  resistance,  is  designated  by  r,  and  the 
line  potential  by  £,  the  current  flowing  in  the  armature,  there- 
fore is: 

T          N 

' 


77  jn/  v  ' 

,  _    £  —  -c     _  (R  //  p          60 


1  See  "Some  Practical  Formulae  for  Street-Car  Motors,"  by  Thorburn  Reid, 
Electrical  Engineer,  vol.  xii.  p.  688  (December  23,  1891);  "  Capacity  of  Rail- 
way Motors,"  by  E.  A.  Merrill,  Electrical  Engineer,  vol.  xvii.  p.  231  (March 
14,  1894). 


§  117]  CALCULATION  OF  ELECTRIC  MOTORS.  439 

and  solving  for  /,  we  have  : 

7  =  "        Nc  x  ^se~   ~1          ^~       7  ' 
r  +      ^^;XX   6oXl° 


Hence  the  work  done  by  the  motor: 

N  y  N         P       N 
^  =  *'x/=-^-5x  -,-x^ 


(397) 


7VC,  ^Ygg,  and  «'p  are  constants  of  the  motor,  and  (R'  varies 
somewhat  with  the  saturation  of  the  field,  but  may  be  consid- 
ered practically  constant;  if,  therefore,  we  unite  all  constants 
by  substituting: 

_  Ne    X    ^e         i         io8 
~W~        <  W;  Xto  ' 

the  above  formulae  (395),  (396),  and  (397)  become: 

£'  =  K  X  /X  N,      ..........  (398) 


and 

p  =  Kx  P  x  N  ..........  (400) 

The  value  of  the  constant  K  can  be  readily  calculated  from 
the  windings  of  the  machine  and  from  the  dimensions  and 
flux  densities  of  its  magnetic  circuit.  If,  however,  the  values  of 
E,  /,  and  N  for  any  load  are  given,  and  it  is  required  to  find 
the  counter  E.  M.  Fs.,  the  currents,  and  the  mechanical  out- 
puts for  other  loads,  then  K  can,  far  simpler  and  more  accu- 
rately, be  determined  by  substituting  the  given  values  in: 

E~  /x  r 


which  is  obtained  from  (399)  by  transformation. 

(2)   Speed  of  Motor  for  Given  Car  Velocity. 

The  speed  of  the  motor  required  to  move  the  car  at  a  given 
velocity,  with  a  given  reduction  gear,  is: 


440  DYNAMO-ELECTRIC  MACHINES.  [§  117 

N  _  feet  per  min.  _   5280  x  12  x  ^m  X  s 

4r  60  X  n  X  dw 

12   ' 


in  which  z/m  =  speed  of  car,  in  miles  per  hour; 

2     =  ratio  of  speed  reduction,  /.  ^.,  ratio  of  arma- 

ture revolutions  to  those  of  the  car  axle; 
d^   =  diameter  of  car  wheel,  in  inches. 

(3)    Horizontal  Effort,    and  Capacity  of  Motor   Equipment  for 
Given   Conditions. 

The  power  required  to  propel  a  car  depends  upon  five 
things:  friction,  grade,  condition  of  track,  curvature  of  track, 
and  speed.  No  accurate  formula  can  be  given  for  the  resist- 
ance due  to  friction,  condition  of  track,  and  curvature,  for  this 
resistance  will  vary  largely  at  different  times  with  the  same 
car,  depending  upon  the  care  with  which  the  bearings  and 
gears  are  oiled,  and  whether  the  track  is  wet  or  dry,  clean  or 
dusty,  or  muddy.  A  good  average  practical  value  of  the 
specific  traction  resistance,  verified  by  numerous  tests,  is  30* 
pounds  per  ton  of  weight  on  the  level,  and  (30  ±  20  X  g) 
pounds  per  ton  on  grades,  g  being  the  percentage  of  the  grade, 
that  is,  the  number  of  feet  rise  or  fall,  respectively,  in  a 
length  of  100  feet.  The  horizontal  force  necessary  to  over- 
come the  traction-resistance  caused  by  a  total  weight  of  Wt 
tons,  therefore,  is: 

A  =  Wt  X  (30  ±  20  X  g)  pounds,     ....(403) 

and   the  power,   in   watts,   required   to  exert  this  horizontal 
effort,  at  a  speed  of  #m  miles  per  hour,  will  be: 

pn  _  A  X  ft.  per  min.  X  746 
33,000 


A  x    —  vm  x  746 


§117]  CALCULATION   OF  ELECTRIC  MOTORS. 


441 


In  order  to  facilitate  the  calculation  of  the  propelling  power, 
or  of  the  motor  capacity  required  for  given  conditions  of  trac- 
tion, the  following  Table  CIII.  has  been  calculated,  which 
gives  the  power  required  to  propel  one  ton  at  different  grades 
and  speeds,  and  which,  therefore,  furnishes  P"  by  simply  mul- 
tiplying the  respective  table-value  by  the  total  weight,  Wt 
tons,  to  be  propelled,  /.  ^.,  the  weight  of  car  plus  passengers 
{average  weight  of  passenger  =  125  Ibs.): 

TABLE  GUI.— SPECIFIC  PROPELLING  POWER  REQUIRED  FOR  DIFFERENT 
GRADES  AND  SPEEDS. 


HORSE-POWER  REQUIRED  TO  PROPEL  1  TON, 

PERCENTAGE 

IF  RATED  SPEED  OP  OAR,    Z/m  ,  IN  MILES  PER  HOUR,  is  : 

or  GRADE, 

cr 
& 

8 

10 

12 

15 

18 

20 

25 

30 

0 

.64 

.80 

.96 

1.21 

1.45 

1.61 

2.01 

2.41 

1 

1.07 

1.34 

1.61 

2.01 

2.41 

2.68 

3.35 

4.02 

2 

1.50 

1.88. 

2.25 

2.82 

3.38 

3.76 

4.69 

5.63 

3 

1.93 

2.41 

2.90 

3.62 

4.34 

4.83 

6.03 

7.24 

4 

2.36 

2.95 

3.54 

4.42 

5.31 

5.90 

7.37 

8.85 

5 

2.78 

3.48 

4.17 

5.22 

6.26 

6.97 

8.71 

10.44 

6 

3.22 

4.02 

4.83 

6.03 

7.23 

8.05 

10.04 

12.06 

7 

3.65 

4.56 

5.47 

6.84 

8.20 

9.12 

11.40 

13.67 

8 

4.07 

5.09 

6.11 

7.63 

9.15 

10.18 

12.73 

15.28 

9 

4.50 

5.62 

6.75 

8.43 

10.10 

11.25 

14.07 

16.89 

10 

4.93 

6.16 

7.39 

9.24 

11.07 

12.32 

15.40 

18.50 

12 

5.78 

7.23 

8.68 

10.84 

13.01 

14.47 

18.10 

21.70 

15 

7.07 

8.84 

10.60 

13.25 

15.90 

17.70 

22.10 

26.55 

From  (404)  the  horizontal  pull  required  to   exert  a  given 
power  at  given  speed  is  found  thus: 


Giving  to  hp  values  from  15  to  60  horse-power,  and  to  ?;mfrom 
8  to  30  miles  per  hour,  the  following  Table  CIV.  is  obtained, 
which  at  a  glance  gives  the  horizontal  effort,  or  draw-bar  pull, 
exerted  by  any  motor-capacity  at  a  given  speed,  whereupon, 
from  (403),  the  load  Wt,  in  tons,  can  be  computed,  which  the 
equipment  under  consideration  is  able  to  propel  at  any  given 
grade  : 


442 


DYNAMO-ELECTRIC  MACHINES. 


TABLE  CIV. — HORIZONTAL  EFFORT  OF  MOTORS  OF  VARIOUS  CAPACITIES 
AT  DIFFERENT  SPEEDS. 


RATED 
CAPACITY 

OF 

MOTOR 
EQUIPMENT. 


PULL  AT  PERIPHERY  OP  WHEEL,  A,  IN  POUNDS, 
AT  RATED  SPEED  OP  CAR,    Vm>  IN  MILES  PER  HOUR,  OF  : 


hp 

8 

10 

12 

15 

18 

20 

25 

30 

15 

703 

563 

469 

375 

313 

281 

225 

188 

20 

938 

750 

625 

500 

417 

375 

300 

250 

25 

1,172 

938 

781 

625 

521 

469 

375 

313 

30 

1,406 

1,125 

938 

750 

625 

563 

450 

375 

40 

1,875 

1,500 

1,250 

1,000 

833 

750 

600 

500 

50 

2,344 

1,875 

1,562 

1,250 

1,043 

938 

750 

625 

60 

2,812 

2,250 

1,875 

1,500 

1,250 

1,125 

900 

750 

A  simple  graphical  method  of  determining  the  car  velocity 
and  the  current  consumption  under  various  conditions  of 
traffic  is  shown  in  §  133,  Chapter  XXVIII. 

(4)  Line  Potential  for  Given  Speed  of  Car  and  Grade  of  Track. 

The  E.  M.  F.  required  at  the  motor  terminals  to  drive  a  car 
up  a  particular  grade  at  a  certain  rate  of  speed  may  be  found 
as  follows.  From  (399)  we  have: 

£=S-X(r  +  KxW),      (406) 

in  which  everything  is  known  except  E  and  /.  But  /can  be 
obtained  from  formula  (400),  provided  we  know  the  work  P" 
that  is  to  be  done  by  the  motor  under  the  prevailing  condi- 
tions. The  value  of  P"  being  given  by  (404),  the  current  / 
can  be  expressed  by  transposition  of  formula  (400),  and  by 
substituting  the  expression  so  found  into  (406)  the  required 
E.  M.  F.  is  obtained  : 

'  2  A  X  ft 


E= 


X 


K  X 


..(407) 


Inserting  into  (407)  the  value  of  N  found  from  (402),  we  have : 
304  x  K  X 


X  z 


A  X  4, 
K  X  z  ' 


(408) 


Knowing  E,  we  are  enabled  to  determine  the  size  of  wire 
required  in  the  feeders  to  maintain  a  certain  speed  at  any 
point  on  the  line. 


CHAPTER  XXVI. 

CALCULATION    OF    UNIPOLAR    DYNAMOS. 

418.    Formulae  for  Dimensions  Relative  to  Armature 
Diameter. 

Assuming  the  armature  diameter  of  a  unipolar  dynamo  as 
given,  the  ratio  of  the  working  density  of  the  lines  in  the 
material  chosen  for  the  frame  to  the  flux-density  permissible 
in  the  air  gaps  will  determine  the  dimensions  of  the  frame. 
The  armature  consisting  in  a  solid  iron  or  steel  core  without 
winding,  the  only  air  gap  necessary  is  the  clearance  required 
for  untrue  running,  and,  on  account  of  the  short  air  gaps  so 
obtained,  a  comparatively  high  field  density,  namely,  3C"  = 
40,000  lines  per  square  inch  (or  JC  =  6200  lines  per  square 
centimetre)  can  be  admitted.  The  practical  working  densi- 
ties, as  given  in  Table  LXXVI.,  §  81,  are: 

(&"  —  90,000  lines  per  square  inch  ((&  =  14,000  lines  per  square 

centimetre),  for  wrought  iron, 
®"  —  85,000  lines  per  square  inch  ((B  =  13,200  lines  per  square 

centimetre),  for  cast  steel,  and 
&"  =  45,000  to  40,000  lines  per  square  inch  ((B  =  7000  to  6200 

lines  per  square  centimetre),  for  cast  iron. 

By  comparison,  then,  it  follows  that  the  area  of  the  gap 
spaces  should  be  about  twice  the  cross-section  of  the  frame,  if 
wrought  iron  or  cast  steel  is  used,  and  about  equal  to  the 
frame  section  if  cast  iron  is  employed. 

The  cylinder  type,  on  account  of  its  smaller  diameter  and 
more  compact  form,  being  more  practical  than  the  disc  type  of 
unipolar  machines,  the  former  only  will  here  be  considered, 
inasmuch  as  it  will  not  be  difficult  to  derive  similar  formulae 
for  the  latter.  Moreover,  since  for  the  same  size  of  armature 

443 


444 


DYNAMO-ELECTRIC  MACHINES. 


118 


a  cast-iron  frame  requires  about  twice  the  weight  of  a  cast- 
steel  one,  the  use  of  the  former  material  is  limited  to  special 
cases,  and  formulae  are  given  only  for  machines  having  cast- 
steel  magnets. 

Adopting  the  general  design  indicated  by  Fig.  31,  §  n,  good 
practical  dimensions  of  the  frame  are  obtained  by  making  the 


Fig.  316.  —  Dimensions  of  Cast  Steel  Unipolar  Cylinder  Dynamo. 

active  length  of  the  armature  conductor,  that  is,  the  length  of 
the  poles,  see  Fig  316: 

/P  =  .3<4,     ................  (409) 

<4  being  the  mean  diameter  of  the  armature-cylinder;  and  by 
providing  for  the  winding  an  annular  space  of  length: 

/m  =  .i25da,      ..............  (410) 

and  height: 


The  gap  area,  then,  will  be: 

S8  =  d&  7i  X  .3*4  =  .94*4% 


§118]         CALCULATION  OF   UNIPOLAR  DYNAMOS.  445 

and  the  cross-section  of  the  magnet  frame,  in  order  to  have  a 
magnetic  density  of  85,000  lines  per  square  inch,  must  be-;  - 


The  radial  thickness  of  the  armature,  being  that  of  the  rim 
-of  a  pulley  of  diameter  dM  is  taken  : 

*i  =  .2^,     ....  .........  (412) 

which,  by  adding 

•°5*/4T 

for  clearance,  makes  the  total  distance  between  the  two  pole 
faces  : 

*9  =  .2sV^    .............  (413) 

Allowing  .05  |/^a  for  the  recess  at  the  outer  pole  face,  the 
internal  diameter  of  the  yoke  is  found: 


and  the  diameter  at  the  bottom  of  the  annular  winding  groove, 
or  the  diameter  of  the  magnet  core  is: 

4n  =  d*  -  -25  |/^~-  2  X  .i<4  =  .8</a  --  .25  |/^7 

The  thicknesses  of  the  frame  section  at  these  diameters 
must  be: 


and 


X     7t  .T,     —    .25   tfj~     7t 

-° 


respectively. 

For  the  radial  thicknesses  of  the  outer  and  inner  tube  por 
tions  of  the  field  frame  we  have  the  equations: 


h 

y 


446  DYNAMO-ELECTRIC  MACHINES. 

and 


(.«tfa-.25  |Va  - 
i4  42 


respectively,  from  which  we  obtain,   for  the  radial  thickness 
of  the  yoke : 


=  .  1254  -  .03  4/4,    (416) 

and  for  the  radial  thickness  of  the  core  portion  of  the  frame: 

.34  --.254/4 


2 

=  .264  +  .234/4:      (417) 

The  total  axial  length  of  the  frame  is: 

...(418) 


and  for  the  mean  length  of  the  magnetic  circuit  in  the  frame 
we  find  by  scaling  the  path  : 


119.   Calculation  of  Armature  Diameter   and   Output 
of  Unipolar  Cylinder  Dynamo. 

All  the  dimensions  of  the  machine  being  given,  by  §  118,  as 
multiples  of  the  armature  diameter,  <4  ,  the  dimensioning  of 
the  frame  is  reduced  to  the  calculation  of  d&. 

In  order  to  obtain  a  formula  for  the  armature  diameter,  we 
express  the  polar  area  in  two  ways:  electrically,  as  the  quo- 
tient of  flux,  $,  and  field  density,  OC",  and  geometrically,  as  a 
cylinder  surface  of  diameter  d&  and  length  .3*4. 

The  number  of  parallel  circuits  as  well  as  the  number  of 
conductors  in  the  unipolar  armature  is  unity,  and  the  lines  are 
cut  but  once  in  each  revolution,  the  useful  flux  necessary  to 


§119]         CALCULATION   OF   UNIPOLAR  DYNAMOS.  447 

generate  E  volts  at  the  speed  of  N  revolutions,    therefore, 
from  formula  (137),  §  56,  is: 

_  .6  X&X  *Q9 

~N 

hence  the  gap  area  can  be  expressed,  electrically,  by: 

<£  _  6  x  E  X  io9 

s*  ~  oe"  ~     NX  ae~  ' 

while  geometrically  we  have  from  Fig.  316: 

5g  =  </a  X  TT  X  .3*4  =  .94*4* 
Equating  (420)  and  (421),  we  obtain: 

_6  X  £  X   to9 

•94^a  :       yvr  x  x"    ' 

from  which  follows: 


=  80,000  x      - 


Inserting   in   this  the  value  of  the  field   density   given  in 
118,  namely,  3C"  =  40,000  lines  per  square  inch,  we  find: 


in  which  d&  =  mean  diameter  of  armature,  in  inches; 
E  =  E.  M.  F.  required,  in  volts; 
JV  =  speed^  in  revolutions  per  minute. 

From  (423)  the  armature  diameter  of  a  unipolar  cylinder 
dynamo  can  be  computed  which  generates  the  required  E.  M.  F. 
at  a  given  speed.  If,  however,  the  minimum  value  of  d&  ,  at 
the  maximum  safe  speed  permissible,  is  desired,  JV  must  be 
eliminated  from  the  above  equation  (423),  and  replaced  by  the 
peripheral  velocity.  For  this  purpose  the  value  of  d&  from 
(423)  is  inserted  into  the  equation 

<4  =  230  x  |r  [see  (30),  §  21]; 
by  this  process  we  obtain: 


400  X  V  E  X  JV  =  230  vc , 
or: 


(424) 


DYNAMO-ELECTRIC  MACHINES.  [§  119 

and  this  in  (423)  gives: 


The  values  of  vc,  i.  e.,  the  limiting  safe  velocities,  for  the 
materials  used  in  unipolar  armatures  are: 

vc  =.  400  feet  per  second,  for  forged  steel; 

vc  =  300  feet  per  second,  for  wrought  iron  and  cast  steel ; 

vc  =  200  feet  per  second,  for  cast  iron. 

Inserting  these  values  into  (425),  the  following  formula 
giving  the  minimum  armature  diameter  for  unipolar  cylinder 
dynamos  of  E  volts  E.  M.  F.  are  arrived  at: 

for  forged  steel  armature :      d&  =  -22.  x  E  =  i.  73  E. 

400 

For  wrought-iron  or  cast- 
steel  armature :  d&  =  x  E  =  2. 3  E 

300 

For  cast-iron  armature:          da  =  x  E=  I.AZ  E 

200 

The  corresponding  minimum  speeds  are  found  by  formulae 
(424),  as  follows: 

for  forged  steel  armature:   N  =  .33  X  ^-=— =       °°°. 

E  E 

For  wrought-iron  or  cast- 

steel  armature :  N  =  .  33  X  3-^  =  3°'°00.    \  (±27) 

i 

For  cast-iron  armature :         N  =  .  33  X  — F~  —  -----  . 

E  E       j 

The  output  of  the  machine  is  limited  only  by  the  carrying 
capacity  of  the  armature;  the  current  carrying  cross-section 
of  the  latter  is: 


d&  n  X  .2  V^4  '  =  • 2  K  d , 

and    since    iron    or  steel  will  carry  at  least  200  amperes  per 
square  inch,  the  current  capacity,  in  amperes,  is: 

/=  200  x  .2  n  x  <4*  =  125*4*,     ....(428) 


§120]         CALCULATION  OF   UNIPOLAR  DYNAMOS. 


449 


which,  at  E  volts  E.  M.  F.,  gives  the  output  of  the  dynamo, 
in  watts: 

I 


P  —  E  X  I  —  125  X 


X 


(429) 


120.  Formulae  for  Unipolar  Double  Dynamo. 

In  duplicating  the-  design  shown  in  Fig.  316,  a  unipolar 
dynamo  with  an  armature  of  twice  the  effective  length  of  the 
former  is  obtained,  Fig.  317. 


Fig.  317. — Dimensions  of  Cast-Steel  Unipolar  Double  Dynamo. 

The  pole  area  for  this  type  is: 

Sg  =  2  x  d&n  X  .3*4=  1.88*4',      ....(430) 
hence,  by  equating  (430)  and  (420),  the  diameter  is  obtained: 

~~E~~ 


d&  =  56,400  X 


X  3C 


(431) 


which,  for  JC"  =  40,000  lines  per  square  inch,  becomes: 

<4  =  282X/j/J:. ...(488) 

The  minimum  diameter  which  produces  E  volts  is: 


<4  =  282  X 


J  ^- 
V    -33*>c  " 


490  x~,     ..(433) 

u  f* 


45°  DYNAMO-ELECTRIC  MACHINES.  [§121 

from  which, 

for  forged  steel 


...(434) 


armature:         d&  —  -  —  X  E  =  1.22  £. 

400 
for  wrought-iron 

or       cast-steel 

400 

armature:         d&  =  — —  X  E  =  1.63  E. 
.  .  .  300 

and  for  cast-iron 

armature:         d&  =  -    -  x  £  =  2.45  E. 

For  the  double  machine  the  current  carrying  capacity  and 
the  output  are  found  from  the  same  formulae  (428)  and  (429) 
respectively,  as  for  the  single  frame  machine,  and  since  the 
diameter  of  the  frame  is  smaller,  also  its  current  intensity, 
and,  in  consequence,  its  total  output  will  be  smaller  than 
that  of  a  single  cylinder  machine  of  the  same  E.  M.  F. 

121.   Calculation    of   Magnet    Winding    for    Unipolar 
Cylinder  Dynamos. 

The  dimensions  of  both  the  single  and  double  cylinder 
types  being  generally  expressed  as  multiples  of  the  armature 
diameter,  see  Figs.  316  and  317,  the  magnetizing  forces  re- 
quired for  the  various  portions  of  their  magnetic  circuit  can 
be  computed  from  the  following  formulae. 

The  magnetizing  force  required  for  the  air  gaps,  their 
density  being  3C"  =  40,000,  is: 

ate  =  .3133  X  40,000  x  .05  Vd&  X  1.2  =  750  Vd&,     .  .(435) 

where  1.2   is   taken  to  be  the  probable  factor  of  field  deflec- 
tion, see  Table  LXVL,  §  64. 

Magnetizing  force  required  for  armature: 


x  .2     d*9 

for  wrought  iron:  #4  =  1.5  Vd& 
for  cast  steel:  #/a  =  1.8  Vd& 
for  cast  iron:  at&  =  17.6  Vd& 

Magnetizing  force  required  for  magnet  frame,  cast  steel  of 
density  ®"m  =  85,000: 

«'m  =/ (85,000)  x  i.2</a  =  53<4 (437) 


§121]         CALCULATION  OF    UNIPOLAR  DYNAMOS.  45  l 

There  being  no  armature-reaction,  the  total  number  of 
ampere-turns,  AT,  required  for  excitation  at  full  output,  see 
(227),  §  89,  is  the  sum  of  the  magnetizing  forces  obtained  by 
formulae  (435),  (436),  and  (437). 

The  voltage  of  a  unipolar  dynamo  being  comparatively 
small,  -but  of  constant  value  if  the  speed  is  kept  constant,  the 
excitation  should  be  effected  by  a  shunt-winding. 

The  dimensions  of  the  magnet-coil  being  fixed  by  the 
design,  the  mean  length  of  one  turn,  the  radiating  surface, 
and  the  weight,  respectively,  can  be  expressed  thus: 

/T   -    K   +    /U    *    =    (•*<**    -     .25   Vd&   +    .1,4)    7t 


—  2.  Sid..  —  . 

785  |^Z:    

(438) 

s* 

\J     8. 

——    (4n  ~~f~   2^m 

)   TT    X    /m=   K   -    .25  V^a)  7T    X    .12 

=  .  39^42  —  • 

i  4/^T1"- 

(439) 

and 

wtm 

=   /T    X    /m    X 

^m    X    .21 

-    (2.83*4   - 

•  785  VJ&)  x  .125*4  x  .1*4  x  .21 

=  .oo74^»3  —  .002  Vd<?. 

.f44(N 

The  gauge  of  the  wire,  then,  is  determined  by  means  of 
formula  (319),  and  the  temperature  increase  that  is  obtained 
by  filling  the  entire  space  provided  for  this  purpose,  is  found 
from  (329).  See  example,  §  149. 

If  the  temperature  rise  corresponding  to  the  given  dimen- 
sions should  be  higher  than  desired  in  a  particular  case,  the 
cross-section  of  the  winding  space  must  be  suitably  increased, 
preferably  by  extending  its  length,  /m,  and  a  greater  weight  of 
wire  must  be  employed. 


CHAPTER   XXVII. 

CALCULATION    OF    MOTOR-GENERATORS,   GENERATORS    FOR 
SPECIAL    PURPOSES,   ETC. 

122.  Calculation  of  Motor-Generators. 

A  continuous  current  Motor- Generator,  or  Dynamotor,  or 
Rotary  Transformer,  or  as  it  is  sometimes  also  called,  a  Booster, 
is  the  combination  of  a  motor  and  a  generator  into  one 
machine  for  the  purpose  of  transforming  currents  of  high 
potential  and  low  intensity  into  such  of  low  potential  and  high 
current  intensity,  and  vice  versa.  The  armature  of  a  motor- 
generator  must  therefore  be  provided  with  two  separate  wind- 
ings, each  connected  to  its  own  commutator.  These  two 
armature  windings  may  be  placed  one  above  the  other,  radi- 
ally, or  they  may  be  interspersed.  Since  the  electrical  activity 
of  the  motor  winding  must  be  equal  to  that  of  the  generator 
winding,  the  volume  occupied  by  each  winding  will  be  the 
same,  so  that  half  the  winding  space  of  the  armature  is  appro- 
priated for  each.  The  armature  and  frame  of  a  motor- 
generator  will,  consequently,  be  of-  the  size  and  weight  of 
a  machine  of  double  the  capacity  to  be  transformed. 

Since. the  magnetomotive  force  of  the  motor  armature  wind- 
ing, or  primary  winding,  is  opposite  in  direction  to  that  of  the 
generator  winding,  or  secondary  winding,  and  since  these  two 
magnetomotive  forces  are  nearly  equal  to  each  other  and  are 
produced  in  the  same  core,  they  will  practically  neutralize 
each  other,  the  result  being  that  in  a  motor  generator  there 
is  no  appreciable  armature-reaction,  and  the  brushes  never 
require  to  be  shifted  during  variations  of  load. 

The  size  of  the  machine  depends  upon  the  speed,  the  latter 
being  chosen  with  respect  to  the  heating  of  armature  and 
bearings  only,  for  the  transformation  itself  is  not  influenced 
by  it,  because,  in  calculating  the  motor  portion  of  the  arma- 
ture, any  change  in  the  selection  of  the  speed,  for  the  same 
winding,  calls  for  an  alteration  of  the  field  density  in  exactly 

452 


§122]          CALCULATION  OF  MOTOR-GENERATORS.  453 

the  inverse  proportion,  so  that  the  product  of  conductor- 
velocity  and  field  density  remains  constant,  and  the  E.  -M.  F. 
produced  in  the  generator  winding,  therefore,  is  always  the  same. 

The  field  magnets  of  a  dynamotor  must,  at  least  in  part, 
always  be  excited  from  the  primary  circuit,  that  is,  from  the 
motor  side,  since  otherwise  the  motor  would  not  start.  In 
case  of  transformation  from  low  to  high  tension  the  fields  are 
usually  shunt  wound,  but  in  transforming  from  very  low  to 
high  pressure  it  is  more  economical  to  start  the  motor  action 
by  a  few  turns  of  series  winding  connected  to  the  motor  cir- 
cuit and  to  supply  the  remainder  of  the  field  excitation  by 
a  shunt  winding  from  the  secondary  or  generator  side,  which 
commences  to  be  actuated  as  soon  as  the  machine  has  started 
to  run. 

The  counter  E.  M.  F.  of  the  motor  winding  is  found  by 
deducting  from  the  primary  voltage  the  drop  due  to  internal 
motor  resistance,  and  the  E.  M.  F.  active  in  the  generator 
winding  is  the  sum  of  the  secondary  voltage  required  and 
of  the  potential  absorbed  by  the  secondary  winding.  The 
quotient  of  these  two  E.  M.  Fs.  gives  the  ratio  of  the  number 
of  armature  turns  of  the  primary  to  that  needed  in  the 
secondary  winding.  The  active  length  and  the  cross-section 
of  either  the  primary  or  the  secondary  armature  conductor  is 
then  calculated  in  the  ordinary  manner,  and  the  winding  so 
obtained  is  arranged  upon  an  armature  of  twice  the  winding 
space  necessary  to  accommodate  it.  The  number  of  con- 
ductors and  the  area  of  the  other  winding,  then,  is  simply 
obtained  in  multiplying  or  dividing,  respectively,  by  the  ratio 
of  the  E.  M.  Fs.  to  be  induced  in  the  two  windings.  For 
practical  example  see  §150. 

If  the  primary  E.  M.  F.  be  El  volts,  the  primary  current  /, 
amperes,  the  resistance  of  the  primary  winding  rl  ohms,  and 
the  number  of  primary  armature  turns  7Vai ,  while  the  cor- 
responding quantities  in  the  secondary  circuit  are  Et,  7a ,  r2 , 
and  JVaa,  respectively,  the  counter  E.  M.  F.  of  the  primary 
winding  will  be: 

£',  =  ^—7,^, 

and  the  E.  M.  F.  induced  in  the  generator  armature: 


454  DYNAMO-ELECTRIC  MACHINES.  [§  122 

where 


is  the  given  ratio  of  transformation.     The  ratio  of  the  E.  M.  Fs. 
induced  in  the  two  windings,  therefore,  is: 


£'  '      E.-I.r 


But  since  the  weight  of  copper  in  the  two  windings  is 
approximately  equal,  the  drop  in  the  primary  winding  will 
practically  be : 


so  that  the  ratio  of  the  number  of  turns  of  the  secondary  to 
that  of  the  primary  winding  becomes: 

^a,-^    _  k  £t  +  7,  rt 


7.  r, 

' 


The  terminal   E.   M.   F.   of  the   generator  side  can  then   be 
expressed  thus: 


(• 


-/^  =         -2/^.      -(442) 


The  machine,  therefore,  as  far  as  its  efficiency  is  concerned, 
acts  as  though  it  were  a  motor  of  terminal  E.  M.  F. 

E^  =  Ev  X  ^  volts, 

yVai 

with  an  internal  resistance  of  2  rz  ohms,   that  is,  twice  the 
resistance  of  the  secondary  winding. 


§123]         GENERATORS  FOR   SPECIAL  PURPOSES.  455 

123.  Designing  of  Generators  for  Special  Purposes. 

a.   Arc  Light  Machines  (Constant  Current  Generators]. 

Ordinary  arc  lamps  for  commercial  use  are  so  adjusted  that 
the  pressure  required  to  force  the  current  through  the  arc  is 
from  45  to  50  volts.  A  2000  candle-power  lamp  will  then 
require  a  current  intensity  of  about  10  amperes,  a  1200  candle- 
power  lamp  a  current  of  about  6.5  amperes,  and  a  600  candle- 
power  lamp  a  current  of  about  4  amperes.  The  energy 
consumed  in  the  arc  will  therefore  be  about  450  watts  for  each 
2000  candle-power  lamp,  about  300  watts  for  each  1200  candle- 
power  lamp,  and  about  200  watts  for  each  600  candle-power 
lamp.  An  arc  light  dynamo  for  n  lamps  must  therefore  have 
a  capacity  of  450;*,  or  300/2,  or  200;;  watts,  respectively,  and, 
since  arc  lamps  are  usually  arranged  in  series,  must  be  able  to 
give  an  E.  M.  F.  of  from  50  to  u  X  50  volts,  and  a  constant 
current  of  10,  or  £.5,  or  4  amperes,  respectively.  For  search- 
lights and  lighthouse  reflector  lamps  higher  currents  are  used, 
up  to  200  amperes  or  more;  but  only  a  few  of  these  are  ever 
fed  from  the  same  dynamo,  which,  consequently,  is  of  a  com- 
paratively low  voltage. 

For  all  arc  lamps,  however,  the  constancy  of  the  current  is 
essential,  and  in  arc  light  dynamos,  therefore,  the  current 
must  be  kept  practically  constant  for  all  variations  of  load. 
The  problems  to  be  considered  in  the  design  of  constant  cur- 
rent machines  are  so  radically  different  from  those  of  a  con- 
stant potential  dynamo,  that,  in  general,  a  well-designed 
machine  of  the  one  class  will  not  answer  for  the  other. 

The  ordinary  shunt  dynamo  has  the  tendency  to  regulate 
for  constant  current,1  because  the  induced  E.  M.  F. ,  if  the 
magnetic  circuit  is  suitably  dimensioned,  is  proportional  to  the 
ampere-turns  in  the  field,  and  if  the  resistance  and  the  reaction 
of  the  armature  are  negligible,  the  machine  will  at  any  voltage 
just  give  the  ampere-turns  required  to  produce  this  voltage; 
that  is  to  say,  it  will  produce  any  voltage  required  by  the  con- 
ditions of  the  external  circuit.  This  theoretical  condition  is 


1  See  "  Test  of  a  Closed  Coil  Arc  Dynamo,"  by  Professor  R.  B.  Owens  and 
C.  A.  Skinner;  discussion  by  C.  P.  Steinmetz;  Transactions  Am.  Inst.  E.  E., 
vol.  xi.  p.  441  (May  16,  1894);  Electrical  World,  vol.  xxiv.  p.  150  (August  18, 
1894);  Electrical  Engineer,  vol.  xviii.  p.  144  (August  12,  1894). 


45 6  DYNAMO-ELECTRIC  MACHINES.  [§123 

fulfilled  in  practice  if  the  variable  shunt  excitation,  which  for 
low  saturations  is  proportional  to  the  terminal  voltage,  is  aug- 
mented by  the  constant  exciting  force  necessary  to  compensate 
for  the  drop  of  E.  M.  F.  due  to  armature  resistance  and  for  the 
cross  ampere-turns  due  to  armature  reaction.  Thus,  a  shunt 
dynamo  with  a  constant  separate  excitation  will  fulfill  the  con- 
dition of  giving  a  terminal  E.  M.  F.  proportional  to  the  ex- 
ternal resistance,  and  consequently  a  constant  current,  for  all 
voltages  below  the  bend  of  the  magnetic  saturation  curve;  that 
is,  for  all  voltages  for  which  the  magnetic  density  is  below 
25,000  lines  per  square  inch  in  cast  iron,  and  below  70,000 
lines  per  square  inch  in  wrought  iron  or  cast  steel.  (See  Fig. 
256,  §  88). 

Such  a  shunt  machine  will  be  a  constant  current  dynamo, 
and  will  do  very  well  for  feeding  incandescent  lamps  in  series, 
but  will  be  very  unsatisfactory  as  an  arc  light  generator, 
because  it  does  not  regulate  quickly  enough.  If  the  load  is 
changed  suddenly,  as  often  occurs  in  arc  light  working,  it 
would  take  too  long  a  time  before  the  magnetism  changes  to 
the  altered  conditions  of  load  and  excitation,  and  thus  either  a 
sudden  rush  or  a  sudden  decrease  of  current  would  take  place. 
In  an  arc  light  machine  the  current  intensity  must  not  go 
above  or  below  its  normal  value  when  the  load  is  suddenly 
varied;  the  armature,  therefore,  must  regulate  instantly;  that 
is  to  say,  a  small  change  of  the  armature  current  must  essen- 
tially influence  the  effective  field — if  necessary,  destroy  it,  for 
even  when  short-circuiting  the  machine  the  field  may  not  dis- 
appear entirely,  but  may  only  be  so  distorted  as  to  be  ineffective 
with  regard  to  the  terminal  voltage.  Consequently  a  machine 
of  a  large  and  unvariable  field  flux  and  of  very  large  armature 
reaction  is  required,  so  that  the  armature  magnetomotive  force 
is  of  nearly  the  same  magnitude  as  the  field  M.  M.  F.,  and  very 
large  compared  with  the  resultant  effective  M.  M.  F.  necessary 
to  produce  the  magnetism. 

All  successful  arc  light  generators  are  based  upon  this  prin- 
ciple of  regulating  for  constant  current  by  their  armature  re- 
action, and  in  their  design,  therefore,  the  following  conditions, 
which  lead  to  a  great  armature  reaction,  have  to  be  fulfilled 
[see  formulae  (244)  and  (248),  §93]:  (i)  The  number  of  turns 
on  the  armature  must  be  great;  (2)  the  distortion  of  the  field 


§123]         GENERATORS  FOR   SPECIAL   PURPOSES.  457 

must  be  large;  (3)  the  number  of  bifurcations  of  the  armature 
current  must  be  small;  (4)  the  length  of  path  of  the  field  lines 
of  force  in  the  polepieces  must  be  great  and  its  area  small;  (5) 
the  length  of  path  of  the  armature  lines  of  force  in  the  pole- 
pieces  must  be  small  and  its  area  large;  and  (6)  the  polepieces 
must  require  a  high  specific  magnetizing  force.  Conditions 
(i),  (3),  and  (4)  will  be  fulfilled  if  a  ring  armature  of  small 
axial  length,  and  therefore  of  large  diameter,  is  chosen,  and  if 
the  polepieces  are  shaped  so  as  to  have  large  circumferential 
projections;  condition  (2)  points  to  an  armature  with  smooth 
core,  and  condition  (3)  makes  a  bipolar  type  preferable,  while 
(6)  calls  for  high  densities  in  the  polepieces,  and  is  most  nearly 
attained  by  the  use  of  highly  saturated  cast  iron  for  that  part 
of  the  magnetic  circuit.  In  order  to  have  constant  flux,  a  con- 
stant current  dynamo  must  be  series  wound  and  worked  to  very 
high  densities  in  the  magnetic  circuit,  the  latter  being  the  more 
insensitive  to  sudden  changes  in  the  exciting  power  the  higher 
it  is  saturated.  If  wrought  iron  or  cast  steel  is  used  in  the 
magnet  frame  its  cross-section  should  be  so  dimensioned  that 
the  resulting  magnetic  density  has  a  value  between  110,000  and 
120,000  lines  of  force  per  square  inch  (=  17,000  to  18,500  lines 
per  square  centimetre),  and  in  case  of  cast  iron,  between 
60, ooo and  75,000  lines  per  square  inch  (=  9300  to  11,500  lines 
per  square  centimetre).  The  radial  thickness  of  the  armature 
core  should  be  chosen  so  as  to  obtain  in  the  minimum  armature 
cross-section  a  density  of  from  110,000  to  130,000  lines  per 
square  inch  (=  17,000  to  20,000  lines  per  square  centimetre) 
in  case  of  bipolar  machines,  and  from  100,000  to  120,000  lines 
per  square  inch  (=  15,500  to  18,500  lines  per  square  centime- 
tre) for  multipolar  machines.  This  high  saturation  of  the 
armature  is  required  for  still  another  purpose,  viz.,  to  guard 
against  sudden  rise  of  the  E.  M.  F.  when  the  armature  current 
is  broken.  For,  since  the  magnetomotive  force  effective  in 
producing  the  field  magnetism,  if  current  is  flowing  in  the  arma- 
ture, is  the  difference  between  the  total  field  M.  M.  F.  and  the 
armature  M.  M.  F.,  the  effective  M.  M.  F.,  when  the^urrent 
is  broken,  will  rise  by  the  amount  of  the  armature  reaction  and 
become  equal  to  the  total  field  M.  M.  F.  But,  the  total  M. 
M.  F.  being  very  large  compared  with  the  effective  M.  M.  F. 
necessary  to  send  the  normal  flux  through  the  armature,  an 


45 8  DYNAMO-ELECTRIC  MACHINES.  [§123 

enormous  E.  M.  F.  would  be  produced  in  the  moment  of  open- 
ing the  circuit  if  the  saturation  in  the  armature  core  were 
capable  of  a  corresponding  increase.  In  using  the  above  den- 
sities, however,  ever  so  great  an  increase  of  M.  M.  F.  cannot 
raise  the  saturation,  and  thereby  the  voltage,  seriously. 

For  the  reasons  set  forth  in  §43,  open  coil  windings  are  fre- 
quently used  in  arc  light  dynamo  armatures,  although  good 
results  have  also  been  attained  with  closed  coil  windings. 

In  the  manner  explained  in  the  foregoing,  a  machine  can  be 
designed  which  automatically  keeps  the  current  intensity  con- 
stant under  all  loads  without  any  artificial  means;  it  will,  how- 
ever, require  an  enormous  magnetizing  force  on  both  field  and 
armature  in  order  to  obtain  very  close  regulation.  But  if 
artificial  regulation  is  employed,  very  much  less  magnetizing 
force  is  needed,  since  then  only  just  enough  ampere-turns  are 
sufficient  so  as  not  to  get  too  large  a  fluctuation  of  the  arma- 
ture current  by  a  very  sudden  change  of  load  before  the  regu- 
lator can  act;  hence,  the  arc  light  regulator  is  merely  for  the 
purpose  of  making  the  inherent  automatic  regulation  of  the 
machine  still  closer. 

There  are  two  distinct  systems  of  arc  dynamo  regulation :  (i) 
By  generating  the  maximum  voltage  at  all  times,  but  taking 
off  by  the  brushes  only  such  a  portion  of  it  as  is  required  by 
the  load.  This  is  effected  by  shifting  the  brushes  from  the 
neutral  line;  in  a  closed  coil  armature  this  has  the  effect  that 
the  E.  M.  F.  induced  in  some  of  the  coils  is  in  the  opposite 
direction  to  that  induced  in  the  other  coils  in  the  same  half  of 
the  armature,  and  their  algebraical  sum,  consequently,  can  be 
made  any  part  of  the  maximum  E.  M.  F. ;  in  an  open  coil 
armature  the  brushes  in  the  neutral  position  collect  the  current 
from  the  group  of  coils  having  maximum  E.  M.  F.,  by  moving 
them  either  way;  therefore,  groups  will  be  connected  to  the 
brushes  which  have  a  smaller  E.  M.  F.  than  the  maximum 
potential  of  the  machine.  This  method  of  regulation  is  em- 
ployed in  the  Edison,  Thomson-Houston,  Fort  Wayne,  Sperry, 
Western  Electric,  Standard  Electric,  and  Bain  arc  machines. 
(2)  By  changing  the  whole  E.  M.  F.  generated  by  the  dynamos 
as  the  load  varies.  The  E.  M.  F.  depends  upon  the  number 
of  conductors,  the  cutting  speed,  and  the  field  density.  It  is 
impracticable  to  vary  the  former  two  while  the  machine  is  run- 


§123]         GENERATORS  FOR  SPECIAL  PURPOSES.  459 

ning,  but  the  field  density  can  easily  be  adjusted.  The  field 
strength  depends  upon  the  number  of  turns  on  the  magnets~anii 
upon  the  current  passing  through  them,  and  can  therefore  be 
varied  by  changing  either  of  them.  The  variation  of  the  num- 
ber of  field  turns  is  performed  by  automatically  cutting  out,  or 
short-circuiting,  a  portion  of  them,  and  the  regulation  of  the 
field  current,  by  placing  a  variable  shunt  across  the  field  wind- 
ing. The  Excelsior  arc  light  machine  is  regulated  in  the 
former  manner,  while  the  Brush  and  the  Schuyler  dynamos 
have  a  variable  shunt. 

The  employment  of  external  regulation  introduces  another 
problem.  Whether  the  brushes  are  shifted  in  a  constant  field, 
or  whether  they  remain  stationary  in  a  changing  field,  the  posi- 
tion of  the  neutral  line  relative  to  the  brush  contact  diameter 
varies  with  every  change  of  the  load,  and  means  must  be  pro- 
vided to  collect  the  current  without  sparking  in  any  position. 
The  best  solution  of  this  problem  is,  of  course,  to  so  design 
the  dynamo  that  the  field  is  perfectly  uniform  all  around  the 
armature,  for  then  the  brushes  will  actually  commutate  in  any 
position  of  the  field.  To  attain  this,  a  low  density  is  required 
in  the  gap,  from  10,000  to  20,000  lines  per  square  inch  (=  1550 
to  3100  lines  per  square  centimetre);  hence  the  pole  area  must 
be  made  as  great  as  possible  by  large  extending  polepieces.  If 
this  solution  is  not  feasible  in  practice,  but  if  the  resultant  den- 
sity at  any  position  of  the  brush  varies  with  the  amount  of  shift- 
ing necessary  to  bring  the  brush  to  that  position,  sparkless 
commutation  can  be  obtained  by  varying  the  frequency  of  com- 
mutation; that  is,  the  circumferential  width  of  the  brush,  in 
employing  two  brushes  connected  in  parallel,  and  shifting  the 
one  against  the  other. 

b.  Dynamos  for  Electro- Metallurgy. 

For  electroplating,  electrotyping  (galvano-plastics),  electro- 
lytic precipitation  of  metals  (refining  of  crude  metals  and  ex- 
tracting of  metals  from  ores),  electro-smelting  (reduction  of 
metals),  and  for  other  electrolytical  purposes,  low  electromo- 
tive forces  and  very  large  current  intensities  are  requisite,  as 
the  quantity  of  metal  extracted  from  the  electrolyte  depends 
upon  the  intensity  of  the  current  only,  and  not  upon  its  poten- 
tial. The  latter,  however,  affects  the  quality  of  the  deposit, 


460  DYNAMO-ELECTRIC  MACHINES.  [§123 

for,  if  too  great  an  E.  M.  F.  is  permitted,  the  precipitate  will 
not  be  homogeneous.  The  E.  M.  F.  required  for  any  electro- 
lytical  process  is  the  sum  of  the  counter  E.  M.  F.  of  the  elec- 
trolytic cell,  or  the  E.  M.  F.  of  chemical  reaction,  and  the 
drop  of  potential  caused  by  the  resistance  of  the  electrolyte. 

In  dynamos  for  very  low  voltage,  in  order  not  to  reduce  the 
speed  too  much,  as  this  would  unduly  increase  the  weight  and 
cost,  both  the  number  of  convolutions  on  the  armature  and  the 
field  density  must  be  brought  down  to  their  minimum  values. 
Machines  with  weak  fields  give  trouble  in  sparking  on  account 
of  the  armature  reaction;  dynamos  with  few  massive  con- 
ductors and  few  divisions  in  the  commutator  are  subject  to 
sparking,  and  are  liable  to  heat  from  local  eddy  currents.  Elec- 
tro-metallurgical machines,  therefore,  should  be  designed  with 
short  magnetic  circuit,  especially  the  length  of  the  flux-path 
in  the  polepieces  should  be  as  small  as  possible.  The  pole- 
pieces  should  further  have  a  large  cross-section  in  the  direc- 
tion of  the  field  flux,  but  a  small  transverse  area  and  a  great 
length  for  the  lines  of  force  set  up  by  the  armature  current; 
that  is  to  say,  the  armature  itself  should  be  of  small  diameter 
and  of  comparatively  great  length  (hence,  preferably  a  smooth- 
drum  armature),  and  the  polepieces  should  embrace  only  a 
small  portion  of  its  periphery,  and,  if  possible,  be  provided 
with  longitudinal  slots  parallel  to  the  direction  of  the  field  flux. 
In  order  to  avoid  eddy  currents  as  much  as  possible,  a  stranded 
conductor,  or  a  multiplex  winding  (see  §  44),  or  both  com- 
bined, should  be  used,  and  the  poles  should  be  either  ellipti- 
cally  bored,  or  given  slanting  pole  corners,  or,  if  of  wrought 
iron,  should  be  provided  with  cast-iron  tips  (see  §  76).  If  it  is 
desired  to  use  the  machine  for  different  voltages,  the  polepieces 
may  be  designed  in  accordance  with  Fig.  173,  §  76. 

Dynamos  for  electrolytical  purposes  must  be  shunt  wound, 
as  otherwise  they  are  liable  to  have  their  polarity  reversed  by 
the  action  of  the  counter  E.  M.  F. 

In  case  of  bipolar  types  the  field  density  of  metallurgical 
dynamos,  according  to  their  size,  should  range  between  7000 
and  20,000  lines  per  square  inch  (=  noo  to  3100  lines  per 
square  centimetre),  if  the  polepieces  are  of  cast  iron,  and 
between  10,000  and  30,000  lines  per  square  inch  (=  1550  to 
4650  lines  per  square  centimetre),  if  they  are  of  wrought  iron 


§123]         GENERATORS  FOR  SPECIAL  PURPOSES.  461 

or  cast  steel.  For  multipolar  types  the  corresponding  values 
are  9000  to  30,000  lines  per  square  inch  (—  1400  to  4650 
lines  per  square  centimetre),  and  15,000  to  40,000  lines  per 
square  inch  (=  2300  to  6200  lines  per  square  centimetre), 
respectively.  The  densities  employed  in  the  field  frame  are 
slightly  less  than  those  given  in  Table  LXXVI.,  §  81,  namely, 
about  80,000  lines  per  square  inch  (=  12,500  lines  per  square 
centimetre)  for  wrought  iron  and  cast  steel,  and  about  35,000 
lines  per  square  inch  (=  5500  lines  per  square  centimetre) 
for  cast  iron.  The  armature  core  densities  are  given  in 
Table  XXII.,  §  26. 

c.    Generators  for  Charging  Accumulators. 

Owing  to  the  well-known  fact  that  the  counter  E.  M.  F.  of 
a  storage  battery  gradually  rises  about  25  per  cent,  during 
charging,  generators  to  serve  the  purpose  of  charging  accumu- 
lators, in  order  to  keep  the  charging  current  constant,  should 
be  so  designed  that  their  voltage  increases  automatically  with 
increasing  load.  Such  machines,  therefore,  must  be  excited 
by  a  shunt  winding,  and  must  have  a  very  massive  field  frame 
of  consequent  low  magnetic  saturation.  The  former  is  neces- 
sary to  cause  an  automatic  increase  of  the  magnetizing  force 
with  increasing  external  load,  and  the  latter  to  effect  a  cor- 
responding rise  of  the  flux-density,  and  thereby  of  the 
E.  M.  F.  generated  in  the  armature. 

Thus  for  generating  the  minimum  voltage,  at  start  of  the 
charging  period,  the  magnetic  density  in  the  frame  should  be 
from  30,000  to  35,000  lines  per  square  inch  (=  4600  to  5500 
lines  per  square  centimetre)  in  case  of  cast-iron  magnets,  and 
from  70,000  to  80,000  lines  per  square  inch  (=  n,ooo  to 
12,500  lines  per  square  centimetre)  in  case  of  wrought-iron  or 
steel  magnets.  The  armature  should  have  a  smooth  core  of 
large  cross-section,  so  that  the  reluctance  of  the  gap  remains 
constant,  and  therefore  the  total  reluctance  of  the  circuit 
approximately  constant  for  the  entire  range  of  the  magnetiz- 
ing force. 

In  central  station  working  the  usual  practice  is  to  employ 
the  charging  dynamos  also  for  directly  supplying  the  lighting 
circuits,  either  separately  or  by  connecting  them  in  parallel  to 


4  62  D  YNA  MO-EL  E  C  TRIG  MA  CHINES.  [§123 

the  accumulators  at  the  time  of  maximum  load.  In  this  case 
the  dynamos  must  be  capable  (i)  of  supplying  a  constant 
minimum  potential,  namely  the  lamp  pressure,  which  is  not  to 
vary  with  change  of  load,  and  (2)  of  giving  a  voltage  from  25 
to  30  per  cent,  higher,  i.  e. ,  the  charging  E.  M.  F.  which  must 
automatically  regulate  for  variation  of  load.  These  two  con- 
tradictory conditions  can  be  fulfilled  by  designing  a  shunt 
dynamo  of  low  magnetic  density  in  armature  core  and  mag- 
net frame,  and  by  providing  the  armature  core  with  high  teeth 
of  such  peripheral  thickness  that  the  flux  required  for  the 
generation  of  the  lamp-potential  is  sufficient  to  almost  com- 
pletely saturate  the  same,  the  density  in  the  teeth  at  lamp- 
pressure  to  be  130,000  lines  per  square  inch  (=  20,000  lines 
per  square  centimetre)  or  more.  The  reluctance  of  the  gap 
for  light  loads,  up  to  the  lamp-pressure,  will  then  increase 
with  the  load,  and  as  the  magnetizing  force  in  a  weakly  mag- 
netized shunt  dynamo  also  varies  directly  with  the  load,  the 
flux,  and  thereby  the  E.  M.  F.,  will  remain  constant.  But  as 
soon  as  the  saturation  of  the  teeth  is  reached,  that  is  to  say, 
as  soon  as  the  machine  is  used  for  voltages  above  that  of  the 
lighting  circuit,  the  gap  reluctance,  then  being  equivalent  to 
that  of  air,  will  become  constant,  hence  the  E.  M.  F.  of  the 
machine  will  vary  in  direct  proportion  with  the  load,  as  long- 
as  all  parts  of  the  magnetic  circuit  are  well  below  the  point 
of  saturation. 

d.   Machines  for  Very  High  Potentials. 

For  transmission  of  power  to  long  distances,  for  testing  pur- 
poses, and  for  laboratory  work,  dynamos  of  10,000  volts  and 
over  are  sometimes  needed.  Professor  Crocker,1  in  an 
address  before  the  Electrical  Congress,  Chicago,  August  24, 
1893,  has  given  the  chief  points  to  be  observed  in  the  success- 
ful construction  of  such  machines,  as  follows:  (i)  The  insula- 
tionm  ust  be  excellent,  and  for  no  two  parts  that  have  the 
full  potential  between  them  should  measure  less  than  1000 
megohms;  (2)  the  side-mica  of  the  commutator  should  be  at 
least  -  of  an  inch,  and  the  end  insulations  at  least  £  of 


1  "On   Direct  Current   Dynamos   for  Very    High    Potential,"   by   F.    B. 
Crocker,  Electrical  World,  vol.  xxii.  p.  201  (September  9,  1893). 


§  124]       PREVENTION  OF  ARMATURE  REACTION.  4^3 

an  inch  thick,  and,  if  possible,  the  surface  distance  at  the 
ends  should  be  increased  by  having  the  insulation  project,  the 
number  of  commutator  divisions  can  then  be  so  chosen  that 
the  potential  between  adjacent  bars  is  100  volts  per  pair 
of  poles;  (3)  hard,  smooth,  and  fine-grained  carbon  brushes 
should  be  used,  as  the  employment  of  metallic  brushes,  owing 
to  the  film  of  the  brush-material  that  is  rubbed  into  the  sur- 
face of  the  mica  insulation,  and  which  at  a  voltage  of  10,000  or 
above,  is  a  sufficiently  good  conductor  to  carry  many  watts  of 
electrical  energy,  would  lead  to  the  destruction  of  the  com- 
mutator; (4)  the  brush-pressure  should  not  be  any  greater 
than  necessary  to  insure  good  contact,  because  otherwise  a 
layer  of  carbon  dust  might  be  produced  on  the  commutator, 
when  a  similar  effect  as  with  metallic  brushes,  but  not  to  the 
same  degree,  would  be  caused;  (5)  the  armature  should  have 
a  slotted  core  (toothed  or  perforated),  and  should  be  wound 
with  double  silk-covered  wire,  the  former  with  the  object  of 
reducing  the  reluctance  of  the  magnetic  circuit  and  enabling 
the  employment  of  very  high  field-densities,  from  i£  to  ij 
those  given  in  Tables  VI.  and  VII.,  §  18;  (6)  the  magnet 
frame  should  be  well  saturated,  densities  of  about  100,000 
lines  per  square  inch  (=  15,500  lines  per  square  centimetre) 
for  wrought  iron  or  cast  steel,  and  of  about  50,000  lines  per 
square  inch  (=  7750  lines  per  square  centimetre)  for  cast  iron 
being  best  suited  for  the  purpose;  (7)  the  potential  of  the 
frame  must  be  kept  at  one-half  the  terminal  E.  M.  F.,  a  con- 
dition which,  however,  is  fulfilled  if  the  machine  is  highly 
insulated;  and  (8)  for  reasons  of  economy,  the  field  excitation 
of  a  high  potential  machine  has  to  be  supplied  by  a  series 
winding,  as  otherwise  the  space  occupied  by  the  covering  of 
the  wire,  and  thereby  the  winding  depth,  would  become  exces- 
sive and  a  waste  of  copper,  besides  increased  labor  and  diffi- 
culty in  handling  the  extremely  fine  wire,  would  result. 

124:.  Prevention  of  Armature-Reaction. 

Not  only  the  heating,  but  also,  even  to  a  higher  degree,  the 
amount  of  sparking  at  the  brushes  limits  the  output  of  an 
armature.  The  increased  sparking  with  rise  of  load  is  due  to 
the  interference  of  the  magnetic  field  set  up  by  the  current 
flowing  in  the  armature,  the  tendency  of  the  latter  being  to 


464  D  YNAMO-ELECTRIC  MA  CHINES.  [§  1 24 

produce  a  cross-magnetization  through  the  armature  core,  at 
right  angles  to  the  useful  lines  of  force,  resulting  in  the  dis- 
tortion of  the  field  of  the  dynamo,  that  is,  in  increased  field 
density  under  the  trailing  pole  corners,  and  in  decreased 
density  under  the  leading  pole-corners;  see  Fig.  140,  §  64,  and 
Fig.  270,  §  93.  This  distortion,  depending  in  a  given 
machine  directly  upon  the  magnetizing  force  of  the  armature, 
naturally  increases  with  the  current  furnished  by  the  dynamo, 
and  the  result  is  that  the  amount  of  shifting  of  the  neutral 
line,  or  diameter  of  commutation,  and  therefore  the  sparking 
at  the  brushes,  increases  with  the  load  on  the  machine.  Con- 
sequently, it  becomes  necessary  to  change  the  position  of  the 
brushes  to  meet  every  variation  in  load,  and  unless  the  pole- 
tips  or  the  armature-teeth  are  saturated  (see  §  22),  a  point  of 
loading  is  soon  reached  for  which  no  diameter  of  sparkless 
commutation  can  be  found,  and  the  output  of  the  machine  has 
reached  a  maximum  at  this  point,  notwithstanding  the  fact  that 
the  load  may  be  below  that  allowed  by  a  safe  heating  limit.  In 
order,  therefore,  to  increase  the  output  of  a  dynamo,  the  arma- 
ture reaction  itself,  or  its  distorting  effects,  must  be  checked. 
Besides  the  means  for  this  purpose  already  alluded  to  in 
§§  22,  76,  and  122,  consisting  in  specially  shaping  the  pole- 
pieces,  the  air  gaps,  and  the  armature  teeth  so  as  to  increase 
the  reluctance  of  the  cross-magnetization  path,  either  perma- 
nently or  proportionably  to  the  load,  three  distinct  methods 
for  preventing  armature  reaction  have  recently  been  devised: 
(a)  Balancing  of  armature  cross-magnetization  by  means  of 
special  field  coils  (Professor  H.  J.  Ryan) ;  (b)  compensation  by 
additional  armature  winding  (Wm.  B.  Sayers);  and  (c)  checking 
of  armature  reaction  by  the  employment  of  auxiliary  magnet 
poles  (Professor  Elihu  Thomson). 

a.   Ryan's  Balancing  Field  Coil  Method. ' 
This   method,  which    in    principle   was    first   suggested   by 
Fischer-Hinnen,2    and    independently   also   by    Professor   G. 

1  "  A  Method  for  Preventing  Armature  Reaction,"  by  Harris  J.  Ryan  and 
Milton   E.    Thompson,   Transactions  Am.  Inst.  E.  E.,  vol.  xii.  p.  84  (March 
•20,  1895);  Electrical  World,  vol.  xx.  p.  325  (November  19,  1892);  Electrical 
Engineer,  vol.  xix.  p.  293  (March  27,  1895). 

2  "  Berechnung  Elektrischer  Gleichstrom  Maschinen,"  by  J.  Fischer-Hinnen, 
Zurich,  1892. 


§  124]       PREVENTION  OF  ARMATURE  REACTION.  465 

Forbes,  Professor  S.  P.  Thompson,  and  W.  H.  Mordey,  con- 
sists, in  general,  in  surrounding  the  armature  with  a  stationary 
winding  exactly  equal  in  its  magnetizing  effects  to  the  arma- 
ture winding,  but  directly  opposed  to  the  latter,  and  thus 
completely  balancing  all  armature-reaction.  It  is  practically 
carried  out  by  placing  a  number  of  balancing  coils,  one  per 
pole,  having  a  total  number  of  turns  equal  to  that  of  the  arma- 
ture, into  longitudinal  slots  cut  into  the  polepieces  parallel  to 
the  shaft,  and  by  connecting  these  coils  in  series  to  the  arma- 
ture, thus  making  their  magnetizing  force  of  equal  number  of 
ampere-turns  as,  but  of  opposite  direction  to,  that  of  the 
armature.  The  two  M.  M.  Fs.  thus  counterbalance  and 
neutralize  each  other,  leaving  the  field-flux  practically  un- 
changed at  all  loads  of  the  machine.  By  this  means  all  spark- 
ing due  to  distortion  of  the  field  is  prevented,  and  only  the 
sparking  due  to  the  self-induction  in  the  short-circuited  coil, 
and  to  the  current  reversal  in  the  same,  is  left.  In  order  to 
check  the  latter,  each  pole-space  is  provided  with  a  commuta- 
tion magnet,  or  lug,  which  is  made  the  centre  of  the  respective 
balancing  coil,  and  which  is  energized  by  an  additional  wind- 
ing consisting  in  a  few  extra  turns  of  the  balancing  coil.  If  no 
current  is  flowing  in  the  armature,  and  therefore  also  the 
balancing  coils  are  without  current,  the  commutation  magnet 
is  not  energized  and  the  field  opposite  the  latter  is  neutral, 
but  as  soon  as  load  is  put  on  the  armature  the  commutation 
lug  is  magnetized  by  the  additional  turns  of  the  balancing  coil, 
and  a  reversing  field  for  the  short-circuited  armature-coil  is 
created;  the  strength  of  this  reversing  field,  being  energized 
by  the  armature  current,  increases  with  the  load,  thus  fulfill- 
ing the  conditions  for  sparkless  commutation. 

Fig.  318  shows  two  half  polepieces  slotted  to  receive  a  bal- 
ancing coil  of  eight  turns,  the  half-turns  being  numbered  con- 
secutively to  indicate  the  manner  in  which  the  coil  is  wound. 
In  Fig.  319  the  field  of  a  bipolar  dynamo  with  commutation 
lugs  and  balancing  coils  is  represented;  the  two  polepieces  in 
this  case  are  in  one  piece,  the  commutation  lugs  being  arranged 
in  the  centre  line.  The  same  effect,  however,  can  be  pro- 
duced by  connecting  each  two  polepieces  by  a  pole-bridge,  Fig. 
320,  or  by  employing  a  special  pole-ring.  Fig.  321,  carrying  the 
commutation  lugs  as  well  as  the  balancing  coils.  In  any  case 


466 


D  YNA  MO-ELECTRIC  MA  CHINES. 


[§124 


the  slots  A  and  B,  adjoining  the  commutation  lugs,  C,  are 
larger  than  the  remaining  slots,  for  the  purpose  of  receiving 
the  extra  turns  for  magnetizing  the  commutation  lugs. 

The  disadvantages  of  this   method  are  (i)   increased  reluct- 


Fig.  318. — Polepiece  Provided  with  Ryan  Balancing  Coils. 

ance  of  the  magnetic  circuit  on  account  of  reducing,  by  virtue 
of  the  slots  for  the  balancing  coils,  the  cross-section  of  the  pole- 
pieces;  this  requires  additional  field-excitation;  (2)  increased 
magnetic  leakage  owing  to  the  close  proximity  of  the  pole-tips, 


Fig-  3I9- — Bipolar  Dynamo  Field  with  Commutation  Lug  and  Ryan  Balancing 

Coils. 

or  to  the  bridging  of  the  pole  spaces,  necessitated  to  form  the 
commutation  lugs;  this  leakage  must  also  be  made  up  by  extra 
field-winding;  (3)  reduction  of  the  ventilating  space  around 
the  armature,  and  consequent  increased  heating  of  the  latter; 
and  (4)  increased  weight  and  cost  of  machine.  The  increase 


§124]       PREVENTION  OF  ARMATURE   REACTION.  467 

in  exciting  power  due  to  (i)  and  (2)  alone  may  be  sufficient  to- 
overcome   an   additional  length   of   air  gap    large   enough  to- 


Fig.  320. — Dynamo  Field  with  Pole  Bridge,    Carrying  Commutation  Lug  for 
Ryan  Balancing  Coil. 

nearly  or  quite  check  the  armature  reaction  without  the  use  of 
balancing  coils. 

b.   Say  erf  Compensating  Armature  Coil  Method. ' 

While  in  the  former  method  the  compensating  coils  are 
placed  on  the  fields,  in  the  present  one  additional  series  wind- 
ings are  put  on  the  armature;  a  series  dynamo  on  this  princi- 
ple, therefore,  requires  no  field  winding  at  all,  and  a  compound 
machine  is  to  be  provided  with  shunt  coils  only.  This  end  is- 
attained  by  connecting  the  main  loops  of  the  armature  to  the 
commutator-bars  by  means  of  connecting  coils  which  form 
open  circuits  except  when  in  contact  with  the  brushes;  then- 


Fig.  321. — Dynamo  Field  Frame  with  Pole-Ring  for  Ryan  Balancing  Coils. 

they  carry  the  whole  armature  current,  and  thus  exercise  their 
function  of  creating  a  sufficient  E.  M.  F.  to  balance  the  self- 


1  "  Reversible  Regenerative  Armatures  and  Short  Air  Space  Dynamos,"  by 
W.  B.  Sayers  ;  Trans.  Tnst.  El.  Eng.,  vol.  xxii.  p.  377  (July,  1893),  and 
vol.  xxiv.  p.  122  (February  14,  1895)  ;  Electrical  Engineer  (London),  vol.  xv. 
(new  series)  p.  191  (February  15,  1895)  ;  Electrician  (London),  vol.  xxxvi. 
p.  341  (January  10,  1896). 


468 


DYNAMO-ELECTRIC  MACHINES. 


[§  124 


induction  of  the  short-circuited  armature  coils.  These  "com- 
mutator-coils" form  loops  under  the  field-poles  and  thereby 
produce  a  forward  field,  which  excites  the  magnets.  By  this 
means  it  is  possible  to  control  sparking,  to  reduce  the  magnetic 
reluctance  of  the  frame  and,  in  consequence,  the  exciting 
power,  and  to  raise  the  weight-efficiency. 

The  sparking  being  under  perfect  control,  the  brushes  in  a 
generator  can  be  placed  backward,  instead  of  giving  them  a 
forward  lead,  and  the  armature-current  consequently  exercises 
a  helpful  magnetizing  action  instead  of  having  a  destroying 
effect  as  in  the  ordinary  case. 

Fig.  322  shows  the  principle  of  this  winding,  A,  A,  being  the 
main  armature  coils,  and  JB,  B,  the  compensating,  or  commuta- 


Fig.  322. — Diagram  of  Sayers' Compensating  Armature  Winding. 

tor  coils.  An  auxiliary  magnet,  or  pole  extension,  C,  having 
a  similar  function  as  the  commutator  lug  in  the  previous 
method,  is  employed  to  supply  the  proper  strength  of  the  re- 
versing field  for  the  short-circuited  armature  coil. 

Sayers  uses  toothed  and  perforated  armature  cores,  placing 
the  main  winding  at  the  bottom  and  the  commutator  coils  at 
the  top  in  each  slot.  In  order  to  keep  down  self-induc- 
tion, the  opening  at  the  top  of  the  slot,  that  is,  the  distance 
between  the  tooth-projections,  should  be  made  as  wide  as  can 
be  done  without  exceeding  the  limit  where  appreciable  loss 
would  occur  through  eddies  in  the  polar  surfaces  of  the  field 
magnets.  For  the  latter  reason  the  width  of  this  opening 
should  not  exceed  i£  times  the  length  of  the  air  space;  Sayers 


§  124]       PREVENTION  OF  ARMATURE  REACTION.  469 

usually  makes  it  about  ij  times  that  length.  The  number  of 
conductors  in  each  slot  must  be  as  small  as  is  consistent  -with 
considerations  of  cost  of  manufacture,  and  since  the  number 
of  commutator  segments  should  be  as  small  as  possible,  it  is 
advantageous  to  connect  the  armature  winding  so  that  the 
conductors  in  two  or  more  pairs  of  slots  form  but  one  coil. 
By  placing  the  conductors  of  opposite  potential,  or  connected 
at  the  time  of  commutation  to  opposite  brushes.,  into  separate 
slots,  the  self-induction  of  the  armature  winding  can  be 
reduced  to  about  one-half. 

For  reversible  motors  the  rocking  arm  carrying  the  brush- 
holders  is  mounted  on  the  shaft  so  as  to  move  freely  between 
two  stops,  the  friction  of  the  brushes,  upon  reversal  of  direc- 
tion, changing  the  position  of  the  brushes  automatically  and 
without  sparking  from  the  stop  at  one  side  to  that  of  the 
other,  the  stops  being  so  adjusted  as  to  keep  the  brushes  in 
proper  position  for  sparkless  commutation. 

While  in  the  case  of  a  generator  it  may  be  inadvisable  tt 
reduce  the  air  space  below  a  given  value  on  account  of  the 
crowding  up  of  lines  due  to  the  large  armature  reaction,  caus- 
ing a  diminution  in  the  total  flux,  in  the  case  of  a  motor  this 
action  can  be  taken  advantage  of,  and  the  air  space  reduced  to 
a  safe  mechanical  clearance;  the  reduction  of  the  total  flux 
due  to  crowding  up  will  then  tend  to  compensate  for  drop  of 
pressure  due  to  dead  resistance,  so  that  in  the  case  of  a  motor 
we  obtain  the  happy  concurrence  of  lightest  weight  and  mini- 
mum cost  with  best  regulating  qualities. 

c.    Thomson's  Auxiliary  Pole  Method* 

By  the  employment  of  auxiliary,  or  blank  poles,  one  between 
each  two  active  or  excited  poles,  the  current  in  the  armature 
is  made  to  react  under  load  to  magnetize  a  portion  of  the  field 
frame  which  at  no  load  is  neutral  or  nearly  so.  The  armature 
reaction  may  thus  be  made  to  give  rise  to  a  magnetic  flux  suf- 
ficient, or  even  more  than  sufficient,  to  compensate  for  its 
diminishing  effect  upon  the  useful  field  flux.  This  result  is 


1  "  Compounding  Dynamos  for  Armature  Reaction,"  by  Elihu  Thomson, 
Trans.  A.  I.  E.  £.,  vol.  xii.  p.  288  (June  26,  1895);  Electrical  Engineer, 
vol.  xx.  p.  35  (July  10,  1895). 


470 


DYNAMO-ELECTRIC  MACHINES. 


125 


accomplished  by  dividing  each  field  pole  into  a  portion  which 
is  left  unwound  and  a  portion  which  is  wound  and  excited  in 
shunt,  or  separate.  At  no  load,  only  the  wound  polar  portions 
act  to  generate  the  open  circuit  E.  M.  F.  ;  as  the  load  is  put 
on,  the  unwound  auxiliary  poles  become  active  in  consequence 
of  a  magnetic  flux  developed  in  them  by  the  armature  current 
itself,  that  is  in  consequence  of  the  armature  M.  M.  F.  The 
disposition  of  the  poles  is  shown  in  Figs.  323  and  324,  the  un- 


N        sL:: 


Figs.  323  and  324. — Magnetic  Circuits  of  Dynamos  with  Thomson  Auxiliary 
Poles,  at  no  Load  and  with  Current  in  Armature. 

wound  poles  being  presented  to  the  armature  at  right  angles 
to  the  useful  field  flux.  Fig.  323  gives  the  magnetic  circuits  at 
no  load  when  the  unwound  poles  are  neutral,  magnetically, 
while  in  Fig.  324  the  grouping  of  the  magnetic  circuits  is  repre- 
sented, if  current  is  flowing  in  the  armature,  the  cross-flux  then 
being  taken  up  by  the  auxiliary  poles  and  led  off  into  the  backs 
of  the  wound  poles,  thereby  strengthening  the  useful  field 
instead  of  weakening  it. 

By  properly  choosing  the  position  and  spread  of  the  auxili- 
ary poles  in  relation  to  that  of  the  main  poles,  and  by  adjust- 
ing the  magnetizing  force  of  the  field  relatively  to  that  of  the 
armature,  the  effect  of  compounding,  or  any  degree  of  over- 
compounding,  may  easily  be  obtained,  or  the  blank  poles  may 
be  made  adjustable  in  position  so  as  to  vary  the  effect  of  the 
armature  M.  M.  F.  upon  them. 

125.  Size  of  Air  Gaps  for  Sparkless  Collection. 

Although  from  the  magnetic  standpoint  as.  small  an  air  gap 
as  possible  is  desired,  the  distance  between  armature  core  and 
polepieces  should  not  be  cut  down  too  much,  for  the  following 


§  125]  SIZE   OF  AIR  GAPS.  47  I 

reasons:  (i)  With  a  very  small  air  space  the  excitation  is  too 
low  to  maintain  a  stiff  field  at  full  load;  (2)  eddy  currents"  be- 
come troublesome;  (3)  a  great  difficulty  arises  in  maintaining 
the  armature  exactly  centred,  which  is  much  more  essential 
in  a  multipolar  than  in  a  bipolar  machine;  and  (4)  dynamos 
constructed  with  a  very  small  air  gap  require  a  larger  angle  of 
lead,  and  do  not  generate  as  high  a  voltage  as  others  of  the 
same  type  having  a  larger  air  gap;  this  is  due  to  the  greater 
armature  reaction,  which  causes  a  greater  distortion  of  the 
lines,  and  owing  to  this  increased  obliquity  of  the  lines,  a  short 
air  gap  may  have  a  greater  reluctance  than  a  longer  one;  in 
fact,  there  is  a  certain  value  for  each  dynamo,  beyond  which 
there  is  no  advantage  in  diminishing  the  air  gap,  as  the  ob- 
liquity of  the  lines  becomes  too  great. 

For  sparkless  collection  of  the  current  the  gaps  should  be 
so  proportioned  that  the  magnetizing  force  required  to  give 
the  correct  flow  of  lines  for  the  normal  voltage  and  speed  is 
the  sum  of  the  magnetizing  force  necessary  to  balance  the 
armature  cross  turns,  and  of  the  magnetizing  force  required  to 
give  a  reversing  field  of  sufficient  strength  to  effect  sparkless 
collection.  If  it  is  less  than  this  amount,  there  will  be  spark- 
ing, while  if  it  is  greater,  the  excess  constitutes  a  useless 
waste  of  energy. 

The  magnetizing  force  necessary  to  produce  the  proper 
strength  of  the  reversing  field  has  been  found  by  Claude  W. 
Hill  '  to  be  11.25  times  the  ampere-turns  per  armature  coil  in 
machines  with  ring  armatures  and  wrought-iron  magnets,  and 
from  26.5  to  29.6  times  the  ampere-turns  per  coil  in  drum 
armatures  of  various  sizes.  Taking  12  and  30  times  the  mag- 
netizing force  of  one  armature  coil,  for  ring  and  drum  arma- 
tures, respectively,  the  length  of  the  air  gaps  for  sparkless 
collection  can  be  derived  as  follows: 

By  (228),  §  90,  the  ampere-turns  needed  for  the  air  gaps  are: 


***  =  -3133  x  oe"  x  i"g  =  .3133  x  JC"  x  £ 

the   magnetizing   force   necessary   to    compensate   armature- 
reactions,   by  (250),  is: 

1  "Armatures  and  Magnet-Coils,"  by   Claude  W.   Hill,   Electrical  Review 
(London),  vol.  xxxvii.  p.  227  (August  23,  1895). 


47 2  DYNAMO-ELECTRIC  MACHINES.  [§126 


and  the  ampere-turns  required  to  produce  the  proper  strength 
of  the  reversing  field  by  means  of  the  above  figures  based 
upon  Hill's  results,  can  be  expressed  by: 

ats  =  12  x  n&  X r>  for  ring  armatures, 

ats  =  30  x  n&  X r,  for  drum  armatures. 

For  sparkless  collection  then  we  must  make: 

afg  =  atv  +  ats, 
or,  for  ring  armatures : 


.3133  x  oe 

N~r     k.  x  a  i' 

=  kn  x  — V-  x  -^-5 (- 12  «a  x  - 

2«p  ISO  2  »'p 

whence: 


and  similarly  for  <£r&0i  armatures: 


126.  Iron  Wire  for  Armature  and  Magnet  Winding. 

Small  dynamos,  up  to  5  KW.  capacity,  are  very  uneconomi- 
cal, for  the  reason  that  the  armature-winding  with  its  binding 
wires  occupies  a  comparatively  large  depth,  which  with  the 
clearance  between  the  finished  armature  and  the  polepieces 
makes  the  air  gaps  unduly  large.  The  leakage  factor,  being 
the  quotient  of  the  total  permeance  (which  in  small  machines 
is  particularly  large  on  account  of  the  comparatively  large  sur- 
faces and  small  distances  in  the  frame)  and  of  the  useful  per- 
meance (which  is  extra  small  owing  to  the  long  air  gaps),  is 
therefore  very  high,  and  a  comparatively  large  exciting  power 
is  required  in  consequence. 


§  126]  IRON   WIRE  FOR    WINDING.  473 

For  the  purpose  of  removing  the  main  cause  of  low  efficiency 
of  small  dynamos,  viz.,  excessive  ratio  of  gap-space  to  arma- 
ture diameter,  it  has  been  repeatedly  suggested  '  to  employ 
iron  wire  for  winding  the  armature.  It  is  certain  that  the 
winding  of  an  armature  with  iron  wire  will  materially  reduce 
the  reluctance  of  the  gap-spaces,  and  thereby  will  economize  in 
-exciting  power,  (i)  directly,  by  lessening  the  total  reluctance 
of  the  magnetic  circuit  of  which  the  air  gap  is  the  predominant 
portion,  and  (2)  indirectly  by  reducing  the  magnetic  leakage 
of  the  machine.  Magnetically,  therefore,  the  use  of  iron  wire 
for  the  armature  coils  offers  a  great  advantage  over  copper. 
Another  advantage  of  employing  iron  wire  for  winding  the 
armatures  of  small  machines  is  the  increase  of  the  total  effect- 
ive length  of  the  armature  conductor  thereby  made  possible. 
In  order  to  limit  the  leakage  across  the  tips  of  the  polepieces, 
the  distance  between  the  pole-corners  must  be  larger  than  the 
length  of  the  two  gaps;  in  small  copper-wound  armatures  this 
distance  therefore  is  excessive  compared  with  large  dynamos, 
even  if  it  is  reduced  so  that  quite  a  good  deal  of  leakage  does 
take  place  across  the  pole-tips;  and,  if  iron  armature  coils  are 
employed,  may  be  considerably  decreased,  thereby  rendering  a 
larger  portion  of  the  armature  circumference  useful,  and  in- 
creasing the  effective  length  of  the  armature  conductor,  while 
the  ratio  of  the  decreased  pole-distance  to  the  gap-length, 
which  then  only  consists  in  the  height  taken  up  by  binding 
and  in  the  mechanical  clearance,  will  even  be  greater,  and  thus 
effect  a  decrease  in  the  percentage  of  leakage  from  pole  to 
pole. 

On  the  other  hand,  the  electrical  resistivity  of  iron  being 
about  six  times  that  of  commercial  copper,  for  the  same  cur- 
rent output  an  iron  wire  of  about  six  times  the  cross-section 
•of  a  copper  wire  will  be  required,  and  this  will  occupy  about 
six  times  the  space  on  the  ends  of  a  drum,  or  in  the  interior  of 
a  ring  armature,  eventually  necessitating  an  increase  in  the 
diameter  of  the  latter.  Since  the  winding  is  very  deep,  and 
consists  of  magnetic  conducting  material,  the  outer  layers 
will  form  a  shorter  path  for  the  magnetic  lines  than  the  inner 
ones,  so  that  only  a  portion  of  the  useful  flux  will  cut  the  inner 


'  See  editorial,  Electrical  Engineer,  vol.  xviii.  p.  150  (August  22,  1894). 


474  DYNAMO-ELECTRIC  MACHINES.  [§126 

layers,  and  the  latter  therefore  will  not  generate  their  full 
share  of  E.  M.  F.  The  presence  of  the  iron  wire  in  the  in- 
terior of  the  ring  armature,  moreover,  would  allow  magnetic 
lines  to  cross  the  internal  ring-space,  and  these,  in  cutting  the 
winding,  would  produce  an  E.  M.  F.  opposite  in  direction  to 
the  E.  M.  F.  of  the  machine,  thus  reducing  the  latter  by  its 
amount.  Finally,  the  total  revolving  mass  of  iron  in  the 
armature  being  greater  in  the  case  of  iron  coils,  both  the  hys- 
teresis and  eddy  current  losses  will  be  in  excess  of  those  in  a 
copper-wound  armature. 

As  to  cost,  the  fine  copper  wire  commonly  used  in  small 
armatures  is  difficult  to  insulate  with  thin  cotton  covering, 
and,  therefore,  expensive  silk  insulation  is  usually  applied, 
while  an  iron  wire  of  six  times  its  area,  that  is,  about  2\ 
times  its  diameter,  may  conveniently  be  insulated  with  the 
cheaper  cotton.  But  since  the  weight  of  the  iron  wire,  on 
account  of  its  sixfold  area  and  of  the  higher  winding  space 
and  consequent  larger  armature-heads,  is  at  least  seven  to  eight 
times  that  of  a  corresponding  copper  winding,  it  is  doubtful 
whether  there  is  a  direct  saving  in  cost  by  the  employment  of 
iron  wire.  Furthermore,  .an  increase  in  the  length  of  arma- 
ture shaft  and  machine-base  being  necessitated  by  the  much 
larger  heads,  while  the  reduction  of  the  gap  reluctance  and  of 
the  magnetic  leakage  effects  a  saving  in  magnet-wire  and  a 
decrease  in  field  frame  area  and  length  of  magnetic  circuit, 
the  cost  of  the  machine  frame  is  influenced  positively  as  well 
as  negatively,  and  it  will  depend  upon  the  circumstances  in 
every  single  case  whether  copper  or  iron  armature  coils  are 
preferable. 

It  has  also  been  recommended  to  use  iron  wire  for  winding 
the  magnet  coils.  In  this  case  the  winding  itself  may  be  con- 
sidered a  part  of  the  magnetic  circuit,  hence  the  cores  may  be 
diminished  in  area  and  the  length  of  the  wire  thereby  reduced, 
but  on  account  of  the  insulation  on  the  winding,  its  reluctivity 
is  much  greater  than  that  of  the  solid  core,  and  the  winding 
therefore  can  only  take  the  place  of  a  portion  of  the  core 
much  smaller  than  itself,  leaving  the  outside  diameter  of  the 
magnet  cores  still  larger  than  if  wound  with  copper  wire. 
Owing  to  this  increase  in  diameter,  the  core  surfaces  are  in- 
creased and  their  distance  apart  is  diminished,  hence  the  per- 


§  126]  IRON    WIRE  FOR    WINDING.  475 

meance  of  the  path  between  them  is  increased  and  rise  for 
greater  leakage  is  given,  unless  the  frame  area,  by  the  simul- 
taneous use  of  iron  for  the  armature  coils,  is  reduced  suffi- 
ciently to  make  up  for  this  increase  in  diameter.  In  case  of  a 
small  shunt-wound  machine,  the  magnet  wire  is  extremely  fine, 
and  the  reduction  of  both  the  number  of  turns  and  their  mean 
length  would  necessitate  the  selection  of  a  still  smaller  sized 
wire  in  order  to  have  a  sufficiently  high  resistance  in  the  field 
coils,  and  then  the  use  of  iron  wire  would  be  particularly 
desirable.  From  these  considerations  it  follows  that  the 
advisability  of  using  iron  wire  for  the  magnet  coils  likewise 
depends  upon  the  circumstances  connected  with  the  machine 
in  question. 

The  fact,  however,  that  various  makers  have  practically 
tried  iron  wire  armature  and  magnet  windings  without  adopt- 
ing their  use  for  small  dynamos,  seems  to  indicate  that  there 
is  nothing  to  be  gained  by  the  change. 


CHAPTER  XXVIII. 

DYNAMO-GRAPHICS. 

127.  Construction  of  Characteristic  Curves. 

The  majority  of  the  practical  problems  connected  with  the 
construction  of  dynamo-electric  machines  can  readily  be  solved 
graphically,  by  the  use  of  certain  curves,  technically  called 
characteristics,  which  express  the  dependence  upon  one  another 
of  the  various  quantities  involved.  For  distinction  the  curves 
relating  to  quantities  of  the  external  circuit  are  termed  external 
characteristics,  while  those  referring  to  quantities  within  the 
machine  itself  are  known  as  internal  characteristics. 

In  most  problems  the  magnetic  characteristics,  showing  the 
variation  of  the  E.  M.  F.  with  increasing  magnetizing  power, 
is  employed,  and  the  construction  of  this  curve,  from  the  data 
of  the  machine  calculated,  forms,  therefore,  the  fundamental 
problem  of  dynamo-graphics. 

This  problem  is  solved  by  means  of  the  formula  for  the 
total  magnetizing  force  of  the  machine.  Inserting  into  (227) 
the  values  given  in  (228),  (230),  (238),  and  (250),  Chapter 
XVIII.,  we  obtain  for  the  total  number  of  ampere-turns  per 
magnetic  circuit,  in  English  measure: 

A  T  =  atg  -f  at&  -f  atm  -f.  atr 

=  -3133  x  x"  x  rg  +/  (®'a)  x  i\  +  /(«"»)  x  /•» 

4.  k    x  N**P  x    *"  X  a  (445) 

*>B  >    ~^7~        180°  ' ;  I** 

In  order  to  reduce  all  the  terms  of  (445)  to  a  common  basis, 
we  express  the  densities  of  the  lines  in  the  armature  core  and 
in  the  field  frame  by  the  field  density,  thus: 

<B"a  =  OC"  X  %  ,     and    &"m  =  X  X  3C"X    ^  ; 

*\  ,  ^m 

476 


§127]  DYNAMO-GRAPHICS.  477 

where  3C",  (&"ai,($>"m  =  magnetic    densities    in   gaps,    armature 

core,  and  magnet  frame,  respectively; 

S«,  -^a,  ^m  =  areas  of   magnetic  circuit  in  air  gaps, 

armature  core,  and  field  frame; 
/I  —  factor  of  magnetic  leakage. 

And  furthermore,  since  the  trigonometrical  tangent  of  the 
angle  of  lead  is  the  quotient  of  armature  ampere-turns  by 
total  field  ampere-turns,  see  §  93,  we  can  express  the  compen- 
sating ampere-turns  as  a  function  of  3C",  as  follows: 


y      A     W) 

n'p  1 80° 

The  total  number  of  ampere-turns  per  magnetic  circuit,  con- 
sequently, is: 

AT  =  -3133  x  oe"  x  i"s  +  /  fatf  x  -^  j  x  /"a 

+  /  ^  x  oe"  x  ^  x  /"m+  %^  x  Ai?P  •     (446) 


Every  term  being  a  function  of  the  field  density  3C",  a  curve 
for  AT  can  be  obtained  by  plotting  the  curves  for  the  com- 
ponents atg,  at&,  atm,  and  #/r,  for  different  ordinate  values  of 
JC",  and  subsequent  adding  of  the  abscissae.  In  then  trans- 
forming the  ordinates  from  field  density  into  the  correspond- 
ing proportional  values  of  E.  M.  F.,  by  simply  adding  a  new 
scale,  the  magnetic  characteristic  of  the  dynamo  is  obtained, 
which  gives  the  E.  M.  F.  generated  as  a  function  of  the  mag- 
n«tizing  power. 

In  Fig.  325  the  curves  OA,  OB,  OC,  and  OD  give  the 
ampere-turns  required  for  the  air  gaps,  for  the  armature  core, 
for  the  field  frame,  and  for  compensating  the  armature  reac. 
tion,  respectively,  as  the  field  density,  and,  with  it,  the  arma- 
ture- and  frame-density  increases.  OA  is  a  straight  line  owing 
to  the  fact  that  in  air  the  ampere-turns  required  are  proper- 


478 


DYNAMO-ELECTRIC  MACHINES. 


[§127 


tional  to  the  density  desired.  OB  is  the  saturation  curve  for 
laminated  wrought  iron,  and  OCthat  for  the  material  employed 
in  the  field  frame,  for  values  of  the  density  ranging  from  zero 
to  the  maximum  employed  at  the  largest  overload  the  machine 


AMPERE  TURNS 


Fig-  325. — Construction  of  Magnetic  Characteristic  of  Dynamo,  from  its 
Components. 

is  intended  for.  Any  point,  e,  on  the  characteristic  curve  OE 
is  then  obtained  by  adding  all  the  abscissae  of  OA,  OB,  OC, 
and  OD  that  have  the  same  ordinate  Ox,  thus: 

xe  —  xa  -j-  xb  -\-  xc  -f-  xd . 

If  the  magnet  frame  consists  of  two  or  three  different  mate- 
rials, either  two  or  three  distinct  curves,  as  the  case  may  be, 
have  to  be  plotted  instead  of  the  curve  OC,  or  one  single  curve 
may  be  laid  out  in  which  the  addition  of  the  component  abscis- 
sae has  been  made  by  the  formula: 


//Ax  3C' 

./&; 


x  ^ 

°m 


X  /" 


X    ^ 


x 


X 


X    /"c.s.  . 


(447) 


§127] 


D  YNA  MO-  GRA  PHICS. 


479 


In  cases  where  the  armature  reaction  is  small  and  where  the 
magnetic  density  in  the  armature  core  is  low,  that  is,  in  all 
machines  except  those  designed  for  certain  special  purposes 
(see  §  123),  the  curves  OB  and  OD  are  very  nearly  straight 
lines,  and  can  be  united  with  curve  OA  by  means  of  the  approx- 
imate formula: 


*gar 


at* 


=  .3133 


+ 


x 


x 


x 


X/' 


-f  .00001     X    ^Va    X     -— T   X 


2  n 


( 


=  3e"  x    .3133  x  re  +  ^  x  A  x      x  /"a 


.00001   X 


(448) 


thus  simplifying  the  construction  of  the  magnetic  characteris- 
tic into  the  addition  of  the  abscissae  of  but  a  single  curve  and  a 


Fig.  326. — Simplified  Method  of  Constructing  Magnetic  Characteristic. 

single  straight  line.  Formula  (448)  gives  practically  accurate 
results  if  the  mean  density  in  the  armature  core,  §  91,  at  maxi- 
mum load  of  dynamo,  is  within  80,000  lines  per  square  inch,  or 
12,500  lines  per  square  centimetre,  and  if  the  values  of  the 


480 


DYNAMO-ELECTRIC  MACHINES, 


[§127 


constant  k^  for  different  mean  maximum  load  densities  are 
taken  from  the  following  Table  CV. : 

TABLE  CV. — FACTOR  OP  ARMATURE  AMPERE-TURNS  FOR  VARIOUS 
MEAN  FULL-LOAD  DENSITIES. 


ENGLISH  UNITS.     » 

METRIC  UNITS. 

Mean 
Density 
in 
Armature 
Core 
at  Maximum 

Ampere- 
Turns 
per  inch  of 
Magnetic 
Circuit 
in 

Constant 
in 
Approximate 
Formula 
for  Armature 
Ampere  - 

Mean 
Density 
in 
Armature 
Core 
at  Maximum 

Ampere- 
Turns 
per  cm.  of 
Magnetic 
Circuit 
in 

Constant 
in 
Approximate 
Formula 
for  Armature 
Ampere- 

Output. 

Armature 

Turns. 

Output. 

Armature    \        lurn?:_  . 

Lines  p.  sq.  in. 

Core. 

k™~  ~W~ 

Lines  per  cma 

Core. 

/(®a) 

jj     J  v^aj 
20  ~~      (Ba 

25,000 

4.5 

.00018 

4,000 

1.8 

.00045 

30,000 

5.5 

.00018 

5,000 

2.35 

.00047 

35,000 

6.5 

.00019 

6,000 

2.85 

.000475 

40,000 

7.5 

.00019 

7,000 

3.35 

.00048 

45,000 

8.5 

.00019 

8,000 

3.95 

.00049 

50,000 

9.6 

.00019 

9,000 

4.8 

.00053 

55,000 

11.1 

.00020 

10,000 

6.1 

.00061 

60,000 

13 

.00022 

10,500 

7 

.00067 

65,000 

15.7 

.00024 

11,000 

8 

.00073 

70,000 

19.6 

.00028 

11,500 

9.4 

.00082 

75,000 

24.7 

.00033 

12,000 

10.8 

.00090 

80,000 

31.2 

.00039 

12,500 

12 

.00096 

For  calculations  in  metric  units  the  coefficient  of  gap  ampere- 
turns,  .3133,  must  be  replaced  by  .8  (see  §  90),  and  the  value 
.0000645  is  to  De  taken  for  the  factor  of  compensating  am- 
pere-turns, instead  of  .0000 1,  which  has  been  averaged  from  a 
great  number  of  bipolar  and  multipolar  dynamos,  having  drum 
as  well  as  ring,  and  smooth  as  well  as  toothed  and  perforated 
armatures.  In  the  majority  of  cases  the  value  of  this  factor, 
in  English  units,  ranges  between  .0000075  and  .0000125,  while 
the  actual  minimum  and  maximum  limits  found  were  .0000040 
and  .0000160,  respectively.  The  metric  value  is  derived  from 
the  average  in  English  measure  by  multiplying  with  the  number 
of  square  centimetres  in  one  square  inch. 

The  simplified  process  of  constructing  the  characteristic, 
then,  is  as  follows  :  The  value  of  the  combined  magnetizing 
force,  tf/gar,  calculated  from  (448)  for  any  one,  preferably  high, 
value  of  the  field  density,  3C",  is  plotted  as  abscissa  XA,  Fig. 
326,  with  that  value,  XO,  of  3C"  as  ordinate,  and  the  point  A 


§127]  DYNAMO-GRAPHICS.  481 

thus  found  is  connected  with  the  co-ordinate  centre  O,  by  a 
straight  line.  Next  the  saturation  curve  OC  of  the  full  frame 
is  plotted  by  computing 

A  X  K"  X  ^ 

-^m  > 

for  a  series  of  values  of  3C",  and  by  multiplying 


taken  from  Table  LXXXVIII.  or  LXXXIX.,  or  from  Fig. 
259,  for  the  respective  material,  with  the  length  /"m,  of  the 
magnetic  circuit  in  the  field  frame.  In  case  of  a  composition 
frame  this  process  is  to  be  performed  according  to  formula 
(447).  In  now  adding,  by  means  of  a  compass,  the  abscissae 
of  the  line  OA  to  those  of  the  curve  OC,  such  as  CE  =  XA, 
the  curve  OE  results,  which  is  the  required  characteristic. 

Example  :  To  construct  the  characteristic  of  a  bipolar  gen- 
erator of  125  volts  and  160  amperes  at  1200  revolutions  per 
minute,  having  a  ring  armature  and  a  cast-iron  field  frame,  the 
following  data  being  given:  Length  of  magnetic  circuit  in 
cast  iron,  /"m  =  80  inches;  in  armature  core,  l\  —  15  inches;  in 
gap  spaces,  l\  =  i^  inch.  Mean  area  in  cast  iron,  Sm  = 
79  square  inches;  in  armature,  S&  =  50  square  inches;  in  gaps, 
Sg  =  158  square  inches.  Number  of  armature  conductors, 
jiVc  =  216.  Coefficient  of  magnetic  leakage,  /I  =  1.25. 

If  the  field  frame,  as  in  the  present  case,  consists  of  but  one 
material,  the  magnetization  curve  for  that  material  —  of  which 
a  supply  may  be  prepared  for  this  purpose  —  can  be  directly 
utilized.  It  is  only  necessary  to  multiply  the  scale  of  the 
abscissae  by/"m,  and  to  divide  that  of  the  ordinates  by 


in  the  present  case  the  magnetizing  force  per  inch  length  of 
circuit  is  to  be  multiplied  by  80  to  obtain  the  total  number  of 
ampere-turns,  and  the  density  per  square  inch  of  field  frame  is 
to  be  divided  by 


482 


DYNAMO-ELECTRIC  MACHINES. 


[§  127 


in  order  to  reduce  the  ordinates  to  the  corresponding  values  of 
the  field  density.  In  this  manner  the  second  scales  in  Fig. 
327,  marked  " Total  Number  of  Ampere-turns"  and  "Field 


4/m         8000        12000       16000 

TOTAL  NUMBER  OF  AMPERE  TURNS 

Fig.  327.  —  Practical  Example  of  Construction  of  Characteristic. 


Density,"  respectively,  are  obtained,  and  now  the  line  atgar  can 
be  plotted.  For  this  purpose  the  mean  density  in  the  arma- 
ture core  at  maximum  output,  and  from  this  the  value  of  the 
constant  /£20  must  first  be  determined.  From  formula  (138) 
we  have,  for  the  useful  flux,  at  normal  load  : 


6  X  (125  +  5)  X  io9 

-  —  —  !  —    - 


hence, 


216  X    1200 


3,000,000 

=zT,-=-  —  • 

*\  5° 


=  3,000,000  webers, 


60,000  lines  per  square  inch, 


for  which  Table  CV.  gives: 


.00022. 


§  128]  DYNAMO-GRAPHICS.  483 

Calculating  now  the  value  of  ats&T  for  5C"  =  20,000,  we  find 
by  formula  (448) : 

ats&T  =   20,  ooo  1. 3133  X  i  sV  +  .°o°22  X  1.25  X  — —  X    15 

;     i6o\ 

-|-  .00001   X  216  X I 

=   20,000  (.324   -f   .013   -f   .173) 

=  20,000  x  .510  =  10,200  ampere-turns. 

Plotting  this  value  as  abscissa  for  an  ordinate  of  3C"  =  20,000, 
the  point  A  is  obtained,  which,  when  connected  with  the  co- 
ordinate centre  (9,  gives  the  line  OA,  representing  the  sum  of 
the  gap,  armature,  and  compensating  ampere-turns  for  any  field 
density.  The  addition  of  the  abscissa  of  this  line  to  those  of 
the  curve  OB,  which  gives  the  magnetizing  force,  atm  ,  required 
for  the  field  frame,  furnishes  the  re/juired  characteristic.  In 
order  to  read  the  ordinates  in  volts,  a  third  scale  of  ordinates 
is  yet  to  be  added;  since  the  field  density  at  full  load  is 

0  3,OOO,000 

3C    =  -o-  =  —    d> =   19,000, 


this  third  scale  is  obtained  by  placing  "  125  volts  "  opposite 
that  density,  arid  by  subdividing  accordingly,  the  resulting 
scale  giving  the  output  E.  M.  F.  for  varying  magnetizing 
force. 

128.  Modification  in  the  Characteristic  Due  to  Change  of 
Air  Gap.1 

In  practice  it  often  becomes  necessary  to  change  the  length 
of  the  air  gap  in  order  to  secure  sparkless  collection  of  the 
current  (compare  §  125),  and  it  is  then  important  to  investi- 
gate the  influence  of  different  air  gaps  upon  exciting  power  and 
E.  M.  F.  > 

The  characteristic  OBC,  Fig.  328,  for  the  original  air  gap 
constructed  according  to  §  127,  is  replaced  by  the  curve  ABCy 
consisting  of  the  straight-line  portion,  ABt  and  of  the  curved 


1  Brunswick,    L?  Eclair  age   Elec.,    August   31,   1895;   Electrical  World,  vol. 
xxvi.  p.  349  (September  28,  1895). 


484 


DYNAMO-ELECTRIC  MACHINES. 


[§128 


portion,  BC.  Since  for  low  densities  the  magnetizing  force 
required  for  the  iron  portion  of  the  magnetic  circuit  is  very 
small,  the  straight  line  portion,  AB,  can  be  considered  as  the 
magnetizing  force  due  to  the  air  gap  alone,  and  therefore  the 
curved  portion,  BC,  as  the  sum  of  the  elongation,  BD,  of  this 
straight  line  plus  the  magnetizing  force  due  to  the  iron.  Any 


A     0 


K  H         K' 


H' 


Fig.  328. — Conversion  of  Characteristics  for  Different  Air  Gaps. 


change  in  the  length  of  the  air  gaps  will,  consequently,  for  any 
given  ordinate,  OE,  only  alter  the  abscissa,  EF,  of  the  straight 
line  AD,  but  will  leave  unaffected  the  abscissa-difference,  EG, 
between  the  curve  BC  and  the  straight  line  BD.  Hence 
the  new  characteristic  OC'  for  an  increased  air  gap  is  obtained 
by  increasing  the  abscissa  EF  to  EF' ,  in  the  ratio  of  the  old 
to  the  new  air  gap,  and  by  adding  to  the  abscissa  thus  found 
the  original  difference  between  BC  and  BD,  making  F'G  — 
EG.  Then  Off'  is  the  magnetizing  force  required  to  produce 
the  E.  M.  F.  OE,  corresponding  to  the  point  G'  on  the  new 
characteristic;  the  portion  OK'  of  the  magnetizing  force  is  the 
exciting  power  used  for  the  new  air  gap,  and  K'H'  that  for 
the  remaining  parts  of  the  magnetic  circuit,  and  is  therefore 
independent  of  the  air  gap. 


§129]  DYNAMO-GRAPHICS.  4§5 

129.  Determination  of  the  E.  M.  F.  of  a  Shunt  Dy- 
namo for  a  Given  Load. ' 

If  E,  Fig.  329,  is  the  E.  M.  F.  developed  by  the  machine  at 
no  load,  viz. : 

E  =  ^8h  X  rsh , 

and  if  the  E.  M.  F.,  E^  ,  at  a  certain  load  corresponding  to  an 
armature  current  of  /  amperes  is  to  be  found,  draw  OA,  by 
connecting  the  co-ordinate  centre,  <9,  with  the  point  A  on  the 


AMP.TURiNS 


AT, 


AT 


Fig.  329.  —  Determination  of  E.  M.  F.  of  Shunt  Dynamo  for  Given  Load. 

characteristic  corresponding  to  the  E.  M.  F.  E,  then  make  OB 
equal  to  the  total  drop  of  E.  M.  F.  caused  by  the  armature 
current  /,  or 


=  e&  =  /X  ra  +  *r, 

where  /  X  r&  is  the  drop  caused  by  the  armature  resistance 
ra  ,  and  <?r  that  due  to  armature  reaction.  The  latter  may  ap- 
proximately be  taken  as  half  the  former,  /.  e.: 

ev  =  J  7  X  ra  , 
thus  making  the  total  drop 

_  e&  =  1.5  X  /  X  r&. 

1  Picou,  "  Traite  des  Machines  dynamo-electriques." 


486 


DYNAMO-ELECTRIC  MACHINES. 


[§130 


The  point  B  thus  being  located,  draw  BC  \  OA,  and  from 
the  intersection,  C,  of  this  parallel  line  with  the  characteristic 
curve  drop  the  perpendicular  CD  upon  the  axis  of  abscissae. 
The  portion  FD  of  CD,  from  its  intersection,  F,  with  OA  to 
the  axis  of  abscissae,  is  the  required  E.  M.  F.,  DF  —  £lt  while 
OD  =  ATl\s  the  corresponding  exciting  force  of  the  field 
magnets. 

The  characteristic  shows  that  the  drop,  CF,  is  the  greater 
the  lower  the  saturation  of  the  machine. 

130.  Determination  of  the  Number  of  Series  Ampere- 
Turns  for  a  Compound  Dynamo. 

Let  the  E.  M.  F.,  which  is  to  be  kept  constant,  be  repre- 
sented by  E,  Fig.  330.  Draw  EA  parallel  to  the  axis  of 


O     AMP.  TURNS       AT,*  AT 

Fig.  330. — Determination  of  Compound  Winding. 

abscissae,  and  from  A  on  the  characteristic  drop  the  perpen- 
dicular AB.  The  length  OB  then  gives  the  ampere-turns 
required  on  open  circuit,  that  is,  the  shunt  excitation  ATsh. 
If  e&  again  denotes  the  total  drop  of  E.  M.  F.  caused  by  the 
armature  current  at  the  given  load  (see  §  129),  then  in  order 
to  keep  the  external  E.  M.  F.,  E,  constant,  an  internal  E.  M.  F., 
E'  —  E  -f  ea,  must  be  generated.  Drawing  E'C  ||  OB,  and 
CD  J_  OB,  we  find  that  the  latter  requires  a  total  magnetiz- 
ing force  of  OD  =  AT  ampere-turns. 


§131] 


D  YNAMO-GRAPHICS. 


487 


Hence  the  number  of  series  ampere-turns  necessary  for 
compounding: 

BD  =  ATse    =  AT  -  ATsh, 

the  series  excitation  being  the  difference  between  the  total 
number  of  ampere-turns  required  for  the  generation  of  E' 
volts,  and  the  shunt  excitation  needed  for  E  volts. 

131.  Determination  of  Shunt  Regulators.1 

Shunt  regulators  are  employed:  (a)  to  keep  the  output 
E.  M.  F.  constant  at  variable  load  and  constant  speed;  (b)  to 
keep  the  E.  M.  F.  constant  for  variable  speed;  (c)  to  keep 
the  E.  M.  F.  constant  if  both  the  load  and  the  speed  are  var- 
iable; and  (d)  to  effect  any  variation  in  the  E.  M.  F. 

a.   Regulators  for  Shunt  Machines  of  Varying  Load. 

In  Fig.  331,  E  is  the  constant  potential  of  the  dynamo,  rm, 
the  magnet  resistance,  rr,  the  resistance  of  the  shunt  regula- 


O  A  AT  AT' 

Fig-  331- — Shunt  Regulating  Resistance  for  Constant  Potential  at 
Varying  Load. 

tor,  and  Nm  the  number  of  convolutions  per  magnetic  circuit. 
The  dynamo  is   driven  by  a  motor  of  constant  speed,  and  so 


1  "  Losung  einiger  praktischer  Fragen  liber  Gleichstrom-Maschinen  auf 
graphischem  Wege,"  by  J.  Fischer-Hinnen,  Elektrotechn.  Zeitschr.,  vol.  xv.  p. 
397  (July  19,  1894). 


D  YNAMO-ELECTRIC  MA  CHINES.  [§131 

arranged  that  at  full  load  all  resistance  of  the  regulator  is  cut 
out.  The  resistance  is  to  be  found  which  has  to  be  put  in 
series  with  the  field  magnets  in  order  to  keep  the  potential  on 
open  circuit  the  same  as  at  full  load. 

In  the  manner  shown  in  §  129  the  exciting  current  intensi- 
ties, 7m  and  7'm,  at  no  and  full  load,  respectively,  are  first  de- 
termined by  finding  the  magnetizing  forces  AT  and  AT',  for 
the  E.  M.  Fs.  E,  and  E'  —  E  -j-  <? a ,  respectively,  and  divid- 
ing the  same  by  the  given  number  of  shunt-turns,  thus: 

AT  AT' 

/m=^T,     and7m--^r-. 

-ivm  •LV  m 

Then,  according  to  Ohm's  Law: 
E       Nm  > 


=  tan  otl , 


and 


E        Nm  X  E 


...(449) 


The  values  of  rm  and  (rm  -\-  rr)  can  be  directly  found  as  fol- 
lows: In  the  distance  OA  =  Nm  (Fig.  331)  draw  AB  parallel 
to  the  axis  of  the  ordinates;  find  point  F  by  drawing  EF  \  OA 
and  E'F  |  AB\  and  draw  the  lines  OE  and  OF.  These  will 
intersect  AB  in  points  £t  and  E^  ,  respectively,  for  which  hold 
the  following  relations: 


N 
****'"VS 

and: 


The  required  regulating  resistance,  therefore,  is  directly: 


Example:  A  shunt  dynamo  for  100  volt?  and  40  amperes 
having  an  armature  resistance  of  r&  =  .12  ohm,  a  magnet 
winding  of  Nm  =  4200  turns  per  magnetic  circuit,  and  the 
magnetic  characteristic  shown  in  Fig.  332,  is  to  be  provided 
with  a  regulator  for  constant  pressure  at  variable  load. 


§131]  D  YNA  MO-  GRA  PHICS.  489 

The  drop  at  40  amperes  is : 

e&  =  1.5  x  /  X  1\  =  1.5  x  40  X  .12  =  7.2  volts, 

and  the  characteristic  gives,  for  E  —  ioo  and  E'  —  ioo  -|-  7.2 
=  107.2  volts,  respectively: 

Magnetizing  force  at  no  load,  AT  —      8100  ampere-turns; 
Magnetizing  force  at  full  load,  AT'  =   10,500   ampere-turns. 

Hence,  by  (449) : 

Nm  X  E      4200  x  ioo 
'm  +  rt  =  —T7=r-=  -  -5— =51.8  ohms, 


and 


AT 
X 


4200  X   ioo 


AT'  10,500 

rr  =  51.8  —  40.0  =  1 1. 8  ohms. 


—  40.0  ohms, 


Z    60 


ui  -to 


AMPERE  TURNS 

Fig.  332. — Practical  Example  of  Graphical  Determination  of  Shunt 
Regulator  for  Constant  Potential  at  Varying  Load. 

These  values  can  also  be  directly  derived  from  the  charac- 
teristic by  erecting,  at.  OA  —  4200,  the  perpendicular  AB,  and 
by  drawing  the  lines  OE  and  OF\  the  resistances  can  then  be 
read  off  on  AB  from  the  scale  of  ordinates. 


490 


D  YXAMO-ELECTRIC  MA  CHINES. 


b.    Regulators  for  Shunt  Machines  of  Varying  Speed. 

If  N  is  the  normal,  and  N^  the  maximal,  or  minimal  abnor- 
mal speed,  as  the  case  may  be,  then  the  speed  ratio, 


is  greater  or  smaller  than  i,  according  to  whether  the  speed- 
variation  is  in  the  form  of  an  increase  or  of  a  decrease.     In 


E< 


ATJl 


0    NmC 


AT, 


AT 


AT'    ATM 


Fig.  333. — Shunt  Regulating  Resistance  for  Constant  Potential  at  Increasing 

Speed. 

order  to  obtain  the  characteristic  of  the  machine  for  the 
abnormal  speed,  all  ordinates  of  the  original  characteristic,  /, 
must  be  multiplied  by  the  speed-ratio,  //.  The  result  of  this 
multiplication  is  shown  by  curve  II,  Fig.  333,  for  increasing, 
and  by  curve  II,  Fig.  334,  for  decreasing  speed. 

If  the  point  E  on  curve  /,  corresponding  to  the  E.  M.  F. 
at  normal  speed,  N9  is  connected  with  O,  then  the  intersec- 
tion, En9  of  the  line  OE  with  curve  7,  is  the  E.  M.  F.  which 
the  machine  would  yield  at  the  speed  JVl .  For,  in  the  first 
moment,  the  E.  M.  F.  E,  Fig.  333,  on  account  of  the  increased 
speed,  will  rise  to  the  amount  E ';  at  the  same  time,  however, 
the  exciting  current  rises,  and  with  it  the  magnetizing  force 
increases  from  AT  to  A  T',  causing  an  increase  of  the  E.  M.  F. 
to  E" ,  on  account  of  which  the  magnetizing  power  is  further 
increased  to  AT",  and  so  on,  until  at  En  the  equilibrium  is 
reached.  But  the  potential  of  the  machine  is  to  be  kept  con- 


§131] 


D  YNA  MO-  GRA  PHICS. 


49 1 


stant;  for  this  purpose,  that  magnetizing  force,  AT^  is  to  be 
found  which  produces  the  E.  M.  F.  E  at  the  speed  Nl .  This, 
however,  can  be  done  without  the  use  of  curves  II,  which 
therefore  need  not  be  constructed  at  all.  For,  since  the  num- 


Fig.  334- — Shunt  Regulating  Resistance  for  Constant  Potential  at  Decreasing 

Speed. 

ber  of  ampere-turns  required  to  produce  E  volts  at  N^  revolu- 
tions is  identical  with  the  magnetizing  force  needed  to  generate 

E  x  N     _   E_ 
n 


JV, 


volts  at  normal  speed,  IV,  it  follows  that  it  is  only  necessary 
to  draw  EA  J_  OA,  to  make 

AH  =  E.  =   * 


and  to  draw  BE^  \  OA.  The  abscissa  of  the  intersection,  El , 
of  this  parallel  with  the  characteristic  /  is  the  required  number 
of  ampere-turns,  AT^.  The  latter  will  be  smaller  than  AT  if 
n  >  i,  and  greater  if  n  <  i ;  in  the  former  case,  therefore, 
the  excitation  must  be  reduced  by  adding  resistance,  while  in 
the  latter  case  it  must  be  increased  by  cutting  out  resistance. 
ATl  being  known,  the  regulating  resistance  can  be  computed 
as  follows : 
For  Nl  >  N: 

E         E  X  Wm  E^Nm 


AT, 


AT 


492  £>  YNAMO-ELECTRIC  MA  CHINES.  [§131 

whence : 


For  N^  <  N: 


rr 

or: 


-£F--±T\ (451) 


If  at  distance  OC  =  JVm  a  parallel,  CD,  to  the  axis  of 
or  di  nates  is  drawn,  then  resistances  can  be  directly  derived 
graphically,  as  shown  in  Figs.  333  and  334. 

Example:  A  dynamo  of  125  amperes  current  output,  hav- 
ing the  characteristic  OA,  Fig.  335,  is  to  be  regulated  to  give 
a  constant  potential  of  120  volts  for  a  speed  variation  of  9  per 
cent,  below  and  10  per  cent,  above  the  normal  speed;  to  deter- 
mine the  magnet  and  regulator  resistance,  if  at  normal  speed 
a  current  consumption  of  3.2  per  cent,  is  prescribed. 

Under  the  given  conditions  the  speed  ratio  and  correspond- 
ing E.  M.  F.  for  increasing  speed  is: 


n 


N.       N  -\-  o.  10  N  E       120 

=  -~-  =  -  !  —  —  —    -  =  1.  1  ;      E.  =  —  =  -  =  109  volts; 
JV  N  n          i.i 


and  for  decreasing  speed: 
.       N'        N—  0.09  N  „,         E       120 

«'  =  -     =  "  -'       =  '9'  ;    £>  =      =        =-132  volts- 


For  these  E.  M.  Fs.  the  characteristic  furnishes  the  follow- 
ing magnetizing  forces: 

Ampere-turns  at  normal  speed,  AT  =  20,000; 
Ampere-turns  at  maximum  speed,  AT^  —  15,400; 
Ampere-turns  at  minimum  speed,  AT  \  =27,600. 


Hence: 


20,000  .     . 

Nm  — —  5000  convolutions; 


and  consequently: 


§131] 


D  YNAMO-GRAPHICS. 


493 


5000  X  120 
r-  +  r'  =        .5,400        =39-0  ohms. 

5000  X    120 

rm  =  -  =21.8  ohms. 

27,600 

rT  =  39.0  —  21.8  =  17.2  ohms. 

This  value  is  directly  given  by  the  ordinate  scale  in  the  dia- 
gram, Fig.  335,  being  the  distance  between  the  lines  OF  and 


£,=  109  V 


i   0 


> 


^1 


1 


AMPERE  TURNS 


Fig. 


335-—  Practical  Example  of  Graphical  Determination  of  Shunt  Regulator 
for  Constant  Potential  at  Varying  Speed. 


measured  on  the  ordinate  CD,  in  distance  OC  =  Nm  — 
5000  from  the  co-ordinate  centre. 

c.   Regulators  for  Shunt  Machines  of  Varying  Load  and  Varying 

Speed. 

In  this  case  the  required  resistance  must  be  capable  of 
keeping  the  potential  the  same  at  no  load  and  maximum 
speed  as  at  full  load  and  minimum  speed.  The  former  of 
these  two  extreme  cases  —  no  load  and  maximum  speed,  Nl  , 
—  has  already  been  treated  under  subdivision  b\  to  consider 
the  latter  case  —  full  load  and  minimum  speed  —  reference  is 


494 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§131 


had  to  the  open  circuit  curves  I  and  II,  Fig.  336,  for  normal 
speed,  JV,  and  for  minimum  speed,  7V2 ,  respectively. 

If  AT  ampere-turns   are  requisite  to  produce,  at   normal 
speed  and  on  open  circuit,  the  potential,  E,  to  be  regulated, 


AT  AT2 

Fig.  336.  —  Shunt  Regulating  Resi'stance  for  Constant  Potential   at  Variable 
Load  and  Variable  Speed. 

the  magnetizing  force  for  minimum  speed  is  found  by  deter- 
mining the  abscissa  ATZ  for 


on  curve  II,  which  at  the  same  time  also  is  the  abscissa  for 
the  potential 


on  curve  I,  «a  being  the  ratio  of  minimum  to  normal  speed. 
The  value  of  ^7"2can  therefore  be  derived  without  plotting 
curve  II,  by  adding  to  E  the  drop  e&  ,  dividing  the  sum  by 


and  finding  the  abscissa  for  the  potential  so  obtained.  If  the 
magnetizing  force  for  open  circuit  and  maximum  speed  is  A  Tl  , 
the  desired  regulating  resistance  for  variable  load  and  variable 
speed  is: 

....(452) 


where  Nm  is  the  number  of  turns  per  magnetic  circuit. 


§131] 


D  YNAMO-GRAPHICS. 


495 


Example :  A  shunt  dynamo  having  a  potential  of  60  volts, 
a  drop  in  the  armature  of  3  volts,  a  current-intensity  of  30 
amperes,  6  per  cent,  of  which  is  to  be  used  for  excitation  at 
full  load,  and  having  the  characteristic  given  in  Fig.  337,  is  to 


AMPERE  TURNS 


Fig.  337.—  Practical  Example  of  Graphical  Determination  of  Shunt  Regulator 
for  Constant  Potential  at  Varying  Load  and-Varying  Speed. 

be  regulated  for  a  speed  variation  of  10  per  cent,  above  and 
below  normal  speed,  and  for  loads  varying  from  zero  to  full 
capacity. 

For  no  load  and  maximum  speed  we  have  in  this  case: 


N. 


n^N    = 


N  +  . 


E  6° 

=  ~  =  ~  =  54.5  volts, 


^  —  2500  ampere-turns  (from  Fig.  337);  and  for  full  load 
and  minimum  speed: 

&  =  E  +  ea  =  60  +  3  =  63  volts, 


-AT 


N  -  . 


N  N 

^  =  —  =  ~~  =  7°  volts, 


496  DYNAMO-ELECTRIC  MACHINES.  [§131 

AT^  =  5500  ampere-turns  (from  Fig.  337), 

Nm  =  ^  =  ^^  =  1833  convolutions. 

Connecting  the  points  A  and  B,  in  which  the  2500  and  5500 
ampere-turn  lines,  respectively,  intersect  the  6o-volt  line, 
with  the  co-ordinate  centre  O,  and  erecting,  at  OC  =  1833, 
the  perpendicular  CD,  the  intersections  F  and  G  are  obtained, 
and  the  lengths  CF  and  FG  give  the  required  resistances  of 
the  magnet-winding  and  of  the  shunt-regulator,  respectively. 
The  result  thus  found  can  be  checked  by  the  following 
computation: 


E  6°  K 

rm  =  -  -  =  —rr—     -  =  20  ohms, 


7sh         .06  X  50 
rr  =  44  —  20  =  24  ohms; 

or,  directly,  by  formula  (452): 


rr  =  ,833  X  60  X  -        -     =  M  ohms. 


</.   Regulators  for  Varying  the  Potential  of  Shunt  Dynamos. 

The  potential  of  the  machine  is  to  be  adjustable  between 
a  minimum  limit  El  and  a  maximum  limit  .£2,  and  the  ad- 
justed potential  is  to  be  kept  constant  for  varying  load. 
These  conditions  are  fulfilled  by  so  proportioning  the  magnet- 
winding  and  the  regulator-resistance  that  at  full  load  the 
maximum  potential  Et  is  generated  with  the  regulator  cut  out 
entirely,  and  that  at  no  load  the  minimum  potential  El  is  pro- 
duced with  all  the  regulator-resistance  in  circuit. 

From  the  characteristic,  Fig.  338,  the  magnetizing  forces 
ATlt  corresponding  to  the  potential  El  at  no  load,  and  ATt, 
corresponding  to  the  potential  E9  at  full  load,  or  to  the 
internal  E.  M.  F.,  E\  =  E^  -f-  <?a,  are  obtained;  and  if  again 
N^  denotes  the  number  of  field-convolutions  per  magnetic 
circuit,  we  have: 


§  132] 


D  YNAMO-GRAPHICS. 


497 


and 


from  which  follows: 


1 


r,  =  &„ 


(453) 


In  order  to  derive  the  values  of  the  resistances  rm  and  rr 
graphically,  the  points  £lt  on  the  characteristic,  and  E"9t  on 
the  ampere-turn  line  AT^,  are  connected  with  O,  and  a  per- 


Fig-  338. — Shunt  Regulating  Resistance  for  Adjusting  Potential  Between 
Given  Limits  at  Varying  Load. 

pendicular,  AB,  is  erected  upon  the  axis  of  abscissae  at  the 
distance  OA  —  JVm  from  the  ordinate  axis.  Then  the  por- 
tions AC  and  CD  of  AB,  cut  off  by  the  lines  OE\  and  OEl , 
represent  the  required  resistances  rm  and  rr,  respectively. 

132.  Transmission   of  Power    at   Constant    Speed    by 
Means  of  Two  Series  Dynamos.1 

Since  two  exactly  identical  series  machines  do  not  solve  the 
problem  of  transmission  at  constant  speed  with  varying  load, 
it  is  now  to  be  investigated  graphically,  how  generator  and 
motor  must  be  designed,  electrically,  for  that  purpose. 


J.  Fischer-Hinnen,  Elektrotechn.  Zeitschr.,  vol.  xv.  p.  400  (July  19,  1894). 


498 


D  YNA MO-ELECTRIC  MA  CHINES. 


[§132 


Let  I,  Fig.  339,  represent  the  external  characteristic,  giving 
the  E.  M.  F.  as  function  of  the  current  intensity  of  the 
generator,  and  also  of  the  motor  when  run  as  a  generator, 
thereby  indicating  that  both  machines  are  identical  in  design. 


0  CURRENT  INTENSITY  I 

Fig.  339- — External  Characteristics  of  Generator  and  Motor  of  Identical 

Design. 

If  R  is  the  total  resistance  of  both  machines  plus  the  resist- 
ance of  the  line,  the  total  drop  of  E.  M.  F.  at  any  current- 
intensity,  /,  is 

e&  =  I  x  R, 

and  the  E.  M.  F.  at  the  motor  terminals,  therefore: 
E"  —  E  —  I  x  R  volts. 

By  plotting  the  straight  line  Oe&  and  subtracting  the  ordinate 
values  from  those  of  curve  I,  we  obtain  curve  II,  which  repre- 
sents the  external  characteristic  of  the  motor.  The  speed  of 
the  motor  for  any  load  is  then  found  by  taking  its  E.  M.  F. 
E"  at  the  current-intensity,  /,  corresponding  to  that  load, 
from  the  characteristic  II,  and  inserting  it  into  the  formula: 


N"  = 


E"  X  60  X  io8          K"  X 


N1'    X  n*    X 


..(454) 


where   N"  =  speed  of  motor,  at  certain  load; 

E"  =  E.  M.  F.  required  on  motor-terminals  for  that 

load; 
N\  =  number  of  turns  on  the  motor  armature; 


§132]  DYNAMO-GRAPHICS.  499 

n\  —  number  of  bifurcations  of  current  in  armature; 
<&"  =  number  of  useful  lines  of  force; 

K"  —  -j^jj -7-  =  constant   for   motor   under   con- 

.  -N   a   X   n  P 

sideration. 

But  since  the   E.  M.  F.  of   the  generator   is,  with  similar 
denotation: 

j?  —  N  x  N*  x  n  P  x  ^  —  N  x  ^ 
60  X  io8  K 

it  follows: 

1\T  \S  (f) 

•Wf  •*-    "  /^S,  -*^ 


or 


„,  _  K"  X  K  _  K"       N  X 
K  —~      ~-~      X  ~— 


and  formula  (454)  becomes: 
P"       K 


K"       ^         E  -  I  x  R 
~K   X  W  X  ~      ~E~    ~ 


From  this  follows  that  constancy  of  speed  cannot  be  obtained 
by  means  of  two  identical  machines,  for,  in  that  case  we  would 
have  K"  =  K,  and  $"  =  <P,  or 

K"  $> 


for  which  formula  (455)  would  show  that  N"  is  an  inverse 
function  of  £>,  that  is,  of  the  current-intensity,  /,  of  which  the 
flux  is  a  direct  function. 

But  by  making  K"  3>  greater  than  K  <f>"  in  the  same  propor- 
tion as  E  exceeds  E  —  I  x  ^,  constant  speed  at  varying  load 
can  be  attained.  K  and  K"  are  constants  for  the  respective 
machines,  and  therefore  cannot  be  varied  proportional  to  /  ; 
the  flux  £>,  however,  is  a  direct  function  of  the  exciting  power, 
and  is  inversely  proportional  to  the  reluctance  of  the  magnetic 
circuit;  approximate  constancy  of  N\  consequently,  can  be 
produced  (i)  by  making  the  motor  of  a  higher  reluctance  than 


5°° 


D  YNA  MO-ELE C  '1  *RIC  MA  CHINES. 


[§133 


the  generator,  either  by  increasing  the  length  of  the  air  gap 
or  by  reducing  the  section  of  the  iron  in  the  former,  or  (2)  by 
making  the  magnetizing  force  of  the  generator  greater  than 
that  of  the  motor  by  winding  a  greater  number  of  field  turns 
on  its  magnets.  The  proper  way,  however,  is  to  select  for  the 
motor  a  somewhat  smaller  type,  corresponding  to  the  smaller 
capacity  required  for  it,  and  to  so  design  its  magnet  frame, 
air  gap,  and  windings  as  to  create  a  characteristic  whose 
ordinates  for  any  current  intensity  are  proportional  to  the 
corresponding  ordinates  of  curve  II,  Fig.  339. 

133.  Determination  of  Speed  and  Current  Consumption 
of  Railway  Motors  at  Varying  Load.1 

The  speed  of  the  car  and  the  current  required  for  the  motor 
equipment  are  to  be  found  for  different  grades  of  track,  i.  e., 
for  varying  propelling  power. 

To  solve  this  problem,  the  speed  characteristic  of  the  .motor 


0  I'         I  CURRENT  INTENSITY 

Fig.  340. — Speed  Characteristic  of  Railway  Motor. 

— giving  the  motor  speed,  or  still  better,  the  car  velocity,  as 
a  function  of  the  current-intensity — is  plotted. 

Let  Wt  =  total  weight  to  be  propelled,  in  tons; 
vm  =  velocity  of  car,  in  miles  per  hour; 
g  =  grade  of  track,  in  per  cent.,  /.  e.,  number  of  feet  of 
rise  in  a  horizontal  distance  of  100  feet; 


1  J.  Fischer-Hinnen,  Elektrotechn.  Zeitschr.,  vol.  xv.  p.  401  (July  19,  1894). 


§133]  DYNAMO-GRAPHICS.  5O1 

/  =  current  required  to  propel  W^  tons,  at  g%  grade, 

with  a  velocity  of  vm  miles  per  hour; 
E'  =  potential  of  line; 
7/e  =  mean  electrical  efficiency  of  railway  motor; 


then  we  have,  by  formula  (384),  §  117: 

P"         _  2  X   W,  X  vm  X  (39  +  20  X  g) 

=  ~~ 


...(456) 


In  this  vm  is  not  known,  but  since  the  car  velocity  increases  in 
direct   proportion    with   the   current   strength,    /,    it    is    only 


8       10      12      14       16       18       20      22       24 
CURRENT-INTENSITY,  IN  AMP. 

Fig.  341. — Practical  Example  of  Graphical  Determination  of  Car- Velocity  and 
Current-Consumption  at  Different  Grades. 

necessary  to  calculate,  from  (456),  one  value,  /',  for  any  value, 
v'm,  of  the  velocity.  By  plotting  the  result,  the  point  x\ 
Fig.  340,  is  obtained;  and  if  we  now  connect  x'  with  <9,  and 
prolong  the  line  Ox1  until  it  intersects  the  speed-characteristic 
at  x,  the  co-ordinates  of  this  point,  x,  are  the  required  values 
I  and  vm  for  current  consumption  and  car  velocity,  respec- 
tively, for  the  particular  grade  in  question. 

Example:  An  electric  railway  car  of  a  seating  capacity  of 
34  passengers  weighs  2\  tons,  its  electrical  equipment  ij 
tons;  the  average  efficiency  of  the  motors  from  one-fifth  to 


502  DYNAMO-ELECTRIC  MACHINES.  [§133 

full  load  is  82  percent,  and  the  line  potential  is  500  volts. 
Its  speed  characteristic  is  given  in  Fig.  341.  The  car  velocity 
attained  at,  and  the  current  required  for,  different  grades  up 
to  5  per  cent,  is  to  be  determined  for  maximum  load. 

Including  the  conductor  and  motorman,  the  full  carrying 
capacity  of  the  car  is  36  persons,  which,  at  an  average  of  125 
pounds  per  head,  make  a  •  total  load  of  2j  tons;  the  maxi- 
mum weight  to  be  propelled,  therefore,  is: 

Wt  =  2*/2  +  i%  +  2#  =  6  tons. 
Inserting  the  given  data  into  (356),  we  obtain: 

2  x  6  X 


For  vm  =  6.83  miles  per  hour,  the  equation  for  the  current 
takes  the  following  convenient  form: 

/'  =  .02927  x  6.83  x  (30  +  2og)  =  2  x  (3  +  2£), 

from  which,  for  :  g  =  o  %,  i  0,  2  %,  3  #,  4  #,  5  ^ 
we  find:  /'  =    6,      10,    14,    18,    22,    26  amperes. 

In  order  to  derive  therefrom  the  actual  speeds,  and  current 
intensities  corresponding  to  the  same,  a  line  AB,  Fig.  341,  is 
drawn  parallel  to  the  axis  of  abscissae  and  at  a  distance 
OA  =  6.83  from  it.  Upon  this  line  AB  the  points  x\  , 
x\,  ....#',,  corresponding  to  the  above  values  of  /'  are 
found  and  connected  with  O.  Then  the  co-ordinates  of  the 
intersections  #0  ,  xl9  ....^5of  the  lines  Ox'0,  Ox\,  ----  Ox\ 
with  the  characteristic  are  the  required  amounts  of  /and  vm 
for  the  various  grades. 


PART  Vlll 


PRACTICAL  EXAMPLES 
OF  DYNAMO  CALCULATION. 


CHAPTER   XXIX. 

EXAMPLES   OF    CALCULATIONS    FOR    ELECTRIC    GENERATORS. 

134.  Calculation  of  a   Bipolar,   Single  Magnetic  Cir- 
cuit, Smooth  King,  High-Speed  Series  Dynamo: 

10  Kilowatts.    Single  Magnet  Type. 

Cast  Steel  Frame. 
250  Volts.    40  Amps.    1200  Beys.  p.  Min. 

a.    CALCULATION    OF    ARMATURE. 

i.  Length  of  Armature  Conductor.  —  According  to  §  15,  Chap- 
ter III.,  the  percentage  of  polar  arc,  in  this  case,  is  between 
.75  and  .85;  the  machine  being  a  small  one,  we  take  /3l  =  .78, 
for  which,  in  Table  IV.,  §  15,  we  find  a  unit  armature  induc- 
tion of  e  =  64  x  iQ-9  volt  per  foot  per  bifurcation;  and  since 
the  number  of  pairs  of  armature  circuits  in  bipolar  machines 
is  «'p  =  i,  the  total  unit  induction, 


is  also  =  64  X  io~8  volt.  Next  we  consult  Table  V.,  §  17, 
and  Table  VI.,  §  18,  and  obtain,  as  best  adapted  for  the 
machine  under  consideration,  a  mean  conductor  velocity  of 
z/c  =  80  feet  per  second,  and  an  average  field  density  of 
3C"  =  19,000  lines  per  square  inch,  respectively.  The  total 
E.  M.  F.,  finally,  that  must  be  generated  in  order  to  yield  the 
required  250  volts  at  the  brushes  is  found  by  Table  VIII.,  § 
19,  to  be  about  £'  —  250  -f-  .12  x  250  =  280  volts.  Hence 
by  means  of  formula  (26),  §  19,  we  can  now  directly  calculate 
the  length  of  the  active  armature  conductor  required: 

280  X  io8  _  2ftft  f 

Z*-64X  80  X  19,000  ~2Si 

2.    Sectional  Area  of  Armature   Conductor,    and   Selection   of 
Wire.  —  Taking   a   current   density   of   500   circular   rails  per 

s°s 


DYNAMO-ELECTRIC  MACHINES.  [§134 

ampere,  we  find  the  cross-section  of  the  armature  conductor, 
according  to  formula  (27),  §  20: 

da2  =  5°°  *  4°   =  10,000  circular  mils. 

Referring  to  a  wire  gauge  table  we  find  that  a  single  wire  of 
this  area  would  be  rather  too  thick,  and  therefore  difficult  to 
wind  on  a  small  armature;  we  consequently  select  a  gauge 
of  half  the  above  section,  taking  2  No.  15  B.  W.  G.  wires 
having  a  total  sectional  area  of  2  X  5184  =  10,368  circular 
mils.  The  diameter  of  No.  15  B.  W.  G.  wire  is  d&  =  .072* 
bare,  and  (Ta  =  .088"  when  insulated  for  250  volts  with  a  .016" 
double  cotton  covering. 

3.  Diameter  of  Armature  Core.  —  Applying  formula  (30),  §  21, 
the  mean  winding  diameter  of  the  armature,  corresponding 
to  the  given  speed  of  N  •=.  1200  revolutions  per  minute,  is 
found: 

80 


and  from  this  the  core  diameter  can  be  deduced  by  means  of 
Table  IX.,  §  21,  thus: 

<4  =  -98  X  15.3  =  15  inches. 

Approximately,  d&  could  also  have  been  derived  from  Table 
XL,  by  multiplying  the  respective  table-diameter  by  the  ratio 
of  the  table-speed  to  the  speed  prescribed  : 

*  =  ,4x^=14.  6-. 

1200 

4.  Length  of  Armature  Core.  —  The  number  of  wires  per  layer, 
if  the  entire  circumference  of  the  armature  were  to  be  occu- 
pied by  winding,  is  by  formula  (35),  §  23: 


Allowing  16  per  cent,  of  the  circumference  for  spaces  be- 
tween the  coils,  we  have: 

nw  =  .84  x  535  =  448, 


§134]        EXAMPLES   OF  GENERATOR    CALCULATION.         507 

the  exact  result,  449,  being  replaced  by  the  nearest  even_and 
readily  divisible  number.  Table  XVIII.,  §  23,  gives  the  height 
of  the  winding  space,  h  =  .325",  and  Table  XIX.,  §  24,  the 
thickness  of  core  insulation,  a  —  .040",  allowing  .040"  more  for 
binding  (see  p.  75),  by  formula  (39)  the  number  of  layers  is 
obtained: 

=  -325  —  -o80  _ 

.088  6' 

Remembering  that  the  armature  conductor  consists  of  2 
wires  in  parallel,  we  insert  the  values  found  into  formula  (40) 
and  find  the  length  of  the  armature  core: 

12  x  2  x  288 

/a  = =  54  inches. 

448  X  3 

5.  Arrangement  of  Armature  Winding. — The  voltage  of  the 
machine  being  below  300,  the  potential  between  adjacent  com- 
mutator bars  will  be  within  the  limit  of  sparklessness,  if  the 
number  of  armature  coils  is  chosen  between  40  and  60.  There 
are  three  numbers  which  fulfill  this  condition,  viz. : 


«o  =  4*213 

and 


In  practice  that  number  would  have  to  be  taken  for  which 
the  tools,  and  possibly  even  the  entire  commutator,  of  an  ex- 
isting machine  could  be  used;  here,  however,  although  for  the 
smallest  number  the  cost  of  the  commutator  as  well  as  that  of 
winding  and  connecting  would  be  the  lowest,  we  will  take 
nc  —  56,  because  this  number  is  preferable  to  the  others  on 
account  of  the  more  symmetrical  arrangement  of  the  winding 
it  produces.  For,  in  dividing  the  total  number  of  wires  on 
the  armature,  448  X  3  =  1344,  by  the  different  values  of 
nc,  we  obtain  for  the  number  of  wires  per  armature  coil 
the  figures  24,  28,  and  32,  respectively,  and  as  24  =  8  -f-  8  +  8, 
28  =  9  +  9  +  10,  and  32  =  10  -j-  n  -{-  n,  it  follows 


508 


DYNAMO-ELECTRIC  MACHINES. 


134 


that  in  the  first  case  alone  the  number  of  wires  per  layer  is 
uniform,  while  for  each  of  the  two  latter  windings  the  number 
of  wires  in  one  of  the  three  layers  would  differ  by  i  from  the 
other  two.  Substituting,  therefore,  nc  =  56  into  (46)  the 
number  of  convolutions  per  coil  is  obtained: 

448  X  3  _ 


56  x  2 

that  is  to  say,  the  armature  winding  is  composed  of  56  coils, 
each  having  12  turns  of  2  No.  15  B.  W.  G.  wires. 

The  arrangement  of  the  winding  is  shown  by  the  diagram, 
Fig.  342,  which  represents  the  cross-section  of  one  armature 


Fig  342. — Arrangement  of  Armature  Winding,  IO-KW.  Single-Magnet 
Type  Generator. 

coil.  In  order  to  have  both  ends  of  the  coil  terminate  at  the 
outside  layer,  at  the  inner  circumference  of  the  armature,  and 
at  the  commutator  end,  as  is  most  desirable  for  convenience  in 
connecting  and  for  avoidance  of  crossings,  the  centre,  C,  of 
each  coil  must  be  placed  at  the  inner  armature  circumference 
on  the  commutator  end,  and,  starting  from  (7,  one-half, 
€7,  7',  8,  8'. ...  12  must  be  wound  right-handedly,  and  the  other 
half,  C6',  6,  5',  5  ....  i,  left-handedly,  as  indicated.  The  wind- 
ing in  the  interior  of  the  armature  is  shown  arranged  in  five 
layers,  this  being  necessary  on  account  of  the  smaller  interior 
circumference. 


§134]       EXAMPLES  OF  GENERATOR   CALCULATION.         5°9 

6.  Radial  Depth,  Minimum  and  Maximum  Cross- Section,  and 
Average  Magnetic  Density  of  Armature  Core. — The  useful  mag- 
netic flux,  according  to  formula  (138),  §  56,  being 

6  X  280  X  io9 

<P  = —  2,083,000  webers, 

56  X  12  X  1200 

the  radial  depth  of  the  armature  core,  by  (48),  §  26,  is  obtained : 

2,083,000 

b&  = — =  21  inches. 

2  x  80,000  X5j  X  .90 

In  this  the  density  in  the  minimum  core  section  is  taken  at 
the  upper  of  the  limits  prescribed  by  Table  XXII.,  while  the 
ratio  >£2  is  selected  from  Table  XXIII.,  under  the  assumption 
that  .010"  iron  discs  with  oxide  coating  are  employed. 

Subtracting  twice  the  radial  depth  from  the  core  diameter, 
we  find  the  internal  diameter  of  the  armature  core: 

15  —  2  x  2-J  =  9j  inches, 

and  the  arithmetical  mean  of  the  external  and  internal  diame- 
ters is  the  mean  diameter  of  the  core : 

<*'"»=  ^  (15  +  9i)  =  «i  inches. 

Inserting  the  value  of  b&  into  formula  (234),  §  91,  the  maxi- 
mum depth  of  the  armature  core  is  obtained: 


*'a  =  21  X   y  ^|  -  i  =  5.92  inches; 

hence,  by  (232)  and  (233),  the  minimum  and  maximum  cross- 
sections: 

^ai  =  2  X  5-J-  X  2-J  X  .90  =  26.5  square  inches, 
and 

•Si*  —  2  X  5i  X  5.92  x  .90  =  54.7  square  inches, 

respectively.     Dividing  with  these  areas  into  the  useful  flux, 
we  find  the  maximum  and  minimum  densities: 

mn         2,083,000  . 

(B  ai  =     — ^ ==  78,700  lines  per  square  inch, 

and 

(B"a2  =  — — ~ =  38,100  lines  per  square  inch, 

54-7 


510  DYNAMO-ELECTRIC  MACHINES.  [§134 

for  which  Table  LXXXVIIL,  p.   336,  gives  the  specific  mag- 
netizing forces 

/((B"ai)  =  29.5,  and  /((B*aa)  —  7-1  ampere-turns  per  inch. 

According  to  formula  (231),  therefore,  the  mean  specific 
magnetizing  force  is: 

/((B"a)  =  —  (29.5  -j-  7.1)  =  18.3  ampere-turns  per  inch, 

and  to  this,  according  to  Table  LXXXVIIL,   corresponds  an 
average  density  of: 

(&"a  —  68,500  lines  per  square  inch. 

7.  Weight  and  Resistance  of  Armature  Winding;  Insulation 
Resistance  of  Armature. — The  poles  being  situated  exterior  to 
the  armature,  as  in  Fig.  59,  §  27,  formula  (53)  gives  the  total 
length  of  the  armature  conductor: 

Lt  =  *  x  (si  +  '«  +  .3*5  x  *  x  2gg  =  95J  feet 

J  8 

Hence,  by  (58),  p.  iqi,  the  bare  weight  of  the  armature 
winding: 

wt&  =  .00000303  x  10,368  x  955  =  30  pounds. 

The  same  result  can  also  be  obtained  by  means  of  the  specific 
weight  given  in  the  wire  gauge  table;  No.  15  B.  W.  G.  wire 
weighing. 0157  pound  per  foot,  and  two  wires  being  connected 
in  parallel,  we  have: 

wt&  =  2  x  955  X  .0157  =  30  pounds. 

From  this  the  covered  weight  of  the  winding  is  deduced  by 
means  of  formula  (59)  and  Table  XXVI. ,  thus: 

wt'&  =  1.078  x  30  =  32|  pounds. 

The  resistance  of  the  armature  winding,  at  15.5°  C.,  is  ob- 
tained from  (61),  §  29: 

X  955  X  (-^T  I  =  .24  ohm. 


4X2 


§134]        EXAMPLES  OF  GENERATOR   CALCULATION.         511 
By  Fig.  343  the  surface  of  the  armature  core  is : 

2  x  (5^  -f-  2-J)  X  I2-J  X  7t  —  610  square  inches; 

if  oiled  muslin  whose  average  resistivity,  by  Table  XX.,  §  24, 
is  650  megohms  per  square  inch-mil  at  30°  C.,  and  650  -^-  25 
=  26  megohms  per  square  inch-mil  at  100°  C.,  is  employed 
to  make  up  the  40  mils  of  core  insulation  given  by  Table  XIX., 
the  insulation  resistance  of  the  armature  is  found: 

650  x  40 


610 
and 

26  x  40 
610 


=  42.6  megohms  at  30°  C., 
=  1.7  megohm  at  100°  C. 


8.  Energy  Losses  in  Armature,  and  Temperature  Increase. — 
The  energy  dissipated  by  the  armature  winding,  by  formula 
(68),  §  31,  is  found: 

P&  =  1.2  x  4o3  X  .24  =  460  watts. 
The  frequency  is: 

1 200 
2v,  =   — —  =  20  cycles  per  second; 

the  mass  of  iron  in  the  armature  core,  from  (71),  §  32: 

12!  X  n  X  2-J  x  5|  X  .90 
M=-     — i* — £^ z_  —  .292  cubic  feet; 

for  (B"a  =  68,500,  Table  XXIX.  gives  the  hysteresis  factor: 

rf  =  27.3, 
and  Table  XXXIII.,  the  eddy  current  factor: 

£  =  .034. 

Hence,  the  energy  losses  due  to  the  hysteresis  and  eddy  cur- 
rents, from  (73),  p.  112,  and  (76),  p.  120,  respectively: 

Ph  =  27.3  X  20  x  .292  =  160  watts, 
Pe  =  .034  X  2o2  x  .292  =      4  watts. 

By  (65),  p.  107,  then,  the  total  energy  dissipation  in  the 
armature  is: 

PA  —  460  -f  160  -f  4  =  624  watts. 


5r2  DYNAMO-ELECTRIC  MACHINES.  [§  134 

The  heat  generated  by  this  energy,  according  to  (79),   §  34,' 
is  liberated  from  a  radiating  surface  of 

SA  =  2  x  I2-J-  X  n  X  (5j-  +  2-J  -f  i-|)  =  715  square  inches, 
whence  follows  the  rise  in  armature  temperature,  by  (81),  p.  127  : 


the  specific  temperature  increase,  0'a  =  42°  C.,  being  taken 
from  Table  XXXVI.  for  a  peripheral  velocity  of  80  feet  per 
second,  and  for  a  ratio  of  pole  area  to  radiating  surface  of 


Inserting  the  above  value  of  6a  into  formula  (63),  p.  106,  the 
armature  resistance,  hot,  at  15.5  +  36.5  =  52  degrees,  Centi- 
grade, is  obtained  : 


r'a  =  .24  X  I  i  +  ^  1  =  .275  ohm. 

9.  Circumferential  Current  Density,  Safe  Capacity  and  Run- 
ning Value  of  Armature;  Relative  Efficiency  of  Magnetic  Field. — 
From  formula  (84),  §  37,  the  circumferential  current  density 
is  obtained: 

672  x  20  . 

/c  =  — =  285  amperes  per  inch, 

15  X  TT 

for  which  Table  XXXVII.  gives  a  temperature  increase  of  30° 
to  50°  Cent.,  the  result  obtained  being  indeed  within  these 
limits. 

For  the  maximum  safe  capacity  we  find,  by  formula  (88),  §  38, 
and  by  the  use  of  Table  XXXVIII.  : 

p'  =  I52  X  5i  X  .89  x  1.200  X  19,000  X  io-6 
=  23,500  watts, 

and  for  the  running  value  of  the  armature,  by  formula  (90), 
§39: 

P'&  =  -  -  =  .0197  watt  per  pound  of  copper  at  unit 

field  density  (i  line  per  square  inch). 


§134]         EXAMPLES  OF  GENERATOR    CALCULATION.         513 

The  values  of  P'  and  P\  show  that  the  armature  is  a  very 
good  one,  electrically,  for,  according  to  the  former,  an  over- 
load of  over  roo  per  cent,  can  be  stood  without  injury,  and  by 
comparing  the  latter  with  the  respective  limits  of  Table 
XXXIX.  it  is  learned  that  the  inductor  efficiency  is  as  high  as 
in  the  bes_t  modern  dynamos. 

The    relative   efficiency   of  the  magnetic  field,   by  formula 
(155),  §  59,  is: 

X  80  =  14,880  webers  per  watt 


-     at  unit  velocity, 

and,  according  to  Table  LXII.,  page  212,  this  is  within  the 
limits  of  good  design. 

10.    Torque,   Peripheral  Force,  and  Lateral  Thrust  of  Arma- 
ture.— By  means  of  formula  (93),  §  40,  we  obtain  the  torque: 

r  =  — -fr   X  40  X  672  X  2,083,000  =  65.7  foot-pounds. 

and   by   (95),  §  41,  the   force   acting   at   each   armature  con- 
ductor: 

A  =  -7375  X  5r44  *  1°  o-  =.178  pound. 


The  force  tending  to  move  the  armature  toward  the  magnet 
core  is  found  by  formula  (103),  §  42;  the  reluctance  of  the 
path  through  the  averted  half  of  the  armature  being  about  10 
per  cent,  in  excess  of  that  through  the  armature  half  nearest 
to  the  magnet  core,  the  field  density  in  the  former  will  be 
about  10  per  cent,  smaller  than  in  the  latter;  that  is  to  say, 
the  stronger  density,  3C",  is  about  5  per  cent,  above,  and  the 
weaker  density,  3C"2,  about  5  per  cent,  below  the  average  den- 
sity OC",  or 

iJC",  =  19,000  X  1.05  =  20,000, 
and  JC"2  =  19,000  x  -95  =  18,000; 

hence  the  side  thrust: 

/t  =  ii   X   io-9  X   15   X  5i  X  (20,ooo2  -  18,000')    • 
=  64J  pounds. 


D  YNA  MO-ELECTRIC  MA  CHINES. 


[§134 


This  pull  is  to  be  added  to  or  subtracted  from  the  belt  pull, 
according  to  whether  the  dynamo  is  driven  from  the  magnet 
or  from  the  armature  side. 

ii.   Commutator,    Brushes,    and  Connecting   Cables. — The    in- 
ternal diameter  of  the  wound  armature  being 

9i  —  2  X  (.040  -f  5  x  .088)  =  8J  inches, 
the  brush-surface  diameter  of  the  commutator  is  chosen 
4  =  8J  —  2X$  =  7  inches, 

by  allowing  -f"  radially  for  the  height  of  the  connecting  lugs, 
as  shown  in  Fig.  343.  If  we  make  the  thickness  of  the  side 


Fig.  343.  —  Dimensions  of  Armature  and  Commutator,  IO-KW.  Single-Magnet 

Type  Generator. 

mica  hi  =  .030",  Table  XLVL,  §  48,  and  if  we  fix  the  number 
of  bars  to  be  covered  by  the  brush  as  «k  =  i-J,  the  circum- 
ferential breadth  of  the  brush  contact,  by  (115),  becomes: 


=  -68"' 


Adding  to  this  the  thickness  of  one  side  insulation,  which  is 
also  covered  by  the  brush,  we  obtain  the  breadth  of  the  brush- 
bevel,  .68  +^030  =  71",  which,  for  an  angle  of  contact  of  45°, 
.gives  the  actual  thickness  of  the  brush  as 


—   =      inch. 


Tangential  carbon  brushes  being  best  suited  for  the  machine 
under  consideration,  formula  (118),  page  176,  gives  the  effec- 
tive length  of  the  brush  contact  surface: 


§134]       EXAMPLES  OF  GENERATOR   CALCULATION.         515 


which  we  subdivide  into  two  brushes  of  i  inch  width,  each. 
Allowing  y  between  them  for  their  separation  in  the  holder, 
and  adding  Ty  for  wear,  we  obtain  the  length  of  the  brush- 
surface  from  (114),  page  169,  thus: 

/c  =  2|  X  i-J-  +  TV  =  3;  inches. 

The  best  tension  with  which  the  brushes  are  to  be  pressed 
against  the  commutator  is  found  by  means  of  formulae  (119)  to 
(121)  and  Table  XLVIL,  as  follows: 

The  peripheral  velocity  of  the  commutator  is: 

7  X    TT   X  1200  f 

v^  •=  --  -  =  2200  feet  per  minute, 

hence  the  speed-correction  factor  for  the  specific  friction  pull, 
by  (119),  p.  179: 

22OO   — 


Inserting  the  values  into  (120)  and  (121),  the  formulae  for  the 
energies  absorbed  by  contact  resistance  and  by  friction  re- 
duce to 

/U.  00.68    x£|^=;MJXA, 

and 

Pt  —  6  X  io-5  X  .85  /k  X  2  x  .68  X  2200  =  .i526/k. 

Taking  from  Table  XLVII.  the  values  of  pk  and  /k  for  brush 
tensions  of  i£,  2,  2-J-,  and  3  pounds  per  square  inch,  respec- 
tively, for  tangential  carbon  brush  and  dry  commutator,  we 
find: 


for  i|  Ibs.  per  sq.  in.,  />k  +  Pt  =  3.15  X  .15  '+  ^S26    X     .95 

=  .618  HP.; 

"2         "  "  />k  +  Pt   =   3.15    X    .12    +.1526     X    1.25 

-.569  HP.; 
"  2*  "  "  A  +  Pt  =  3-15  X  .10  +  .1526  X  1.6 

-•559  HP.; 
"  3  "  "  P*  +  Pt  =  3.i5  X  .09  +  .1526  X  1.9 

-•574  HP., 


5l6  DYNAMO-ELECTRIC  MACHINES.  [§  134 

from  which  follows  that  the  most  economical  pressure  is  about 
2J  pounds  per  square  inch  of  contact. 

The  proper  cross-section  of  the  connecting  cables,  by  allow- 
ing 900  square  mils  per  ampere,  in  accordance  with  Table 
XL  VIII.,  §  50,  is  found  to  be: 

40  x  900  =  36,000  square  mils, 
or  36,000  x  —  =  46,000  circular  mils. 

Taking  7   strands   of  3  X  7   wires   each,  or  a  i47-wire  cable, 
each  wire  must  have  an  area  of 

46,000  . 

-  =  315  circular  mils, 
147 

and  the  cable  will  have  to  be  made  up  of  No.  25  B.  £  S.  wire, 
which  is  the  nearest  gauge-number. 

12.  Armature  Shaft  and  Bearings.  —  By  (123)  and  Table  L.,  § 
31,  the  diameter  of  the  core  portion  of  the  shaft  is: 


4  =  t.2  x  =  8,  inches; 

by  (122),  p.  185,  and  Table  XLVIL,  the  journal  diameter: 

<4  =  -003  X  y28o  x  40  X    1/1200  =  1$  inch; 

and,   by    (128),    p.    190,   and  Table  LIV.,  the   length    of   the 
journal: 

/b  =  .1  x  i-J  X  V  I2°o  —  6J  inches. 

13.  Driving  Spokes.  —  Selecting  4-arm  spiders,  similar  to  those 
shown  in  Fig.  127,  §  52,  the  leverage  of  the  smallest  spoke- 
section,  determined  by  the  radial  depth  of  the  armature,  is 
/s  —  3^",  and  the  width  of  the  spokes,  fixed  by  the  length  of 
the  armature  core,  is  b§  =  2";  hence,  by  formula  (126),  p.  189, 
their  thickness: 


§134]       EXAMPLES  OF  GENERATOR   CALCULATION.         51? 

14.  Pulley  and  Belt.  —  Taking  a  belt-speed  of  z>B  =  3500  feet 
per  minute,  Table  LVIIL,  §  54,  the  pulley  diameter  becomes^ 
by  (129),  p.  191: 

inches. 


the  size  of  the  belt,  by  Table  LIX.  : 

/*B  =  -^  inch,  £B  =  4  inches, 
and  the  width  of  the  pulley: 

£p  =  4  -f  1  =  4J  inches. 

b.    DIMENSIONING    OF    MAGNET    FRAME. 

1.  Total  Magnetic  Mux.—From  Table   LXVIIL,  §  70,  the 
average   leakage    factor    for    a     lo-KW    single-magnet   type 
machine,  with  high-speed  drum  armature  and  cast-iron  pole 
pieces,  is  A  =  1.40;  the  present  machine  having  a  ring  arma- 
ture and  a  cast-steel  frame,  the  leakage  is  about  22  -|-  u  —  33 
per  cent,  less   (see  note  to   Table  LXVIIL,  p.  263),  and   the 
leakage  factor  is  reduced  to  A  =  1.27.     The   total  flux,  conse- 
quently, by  (156)  : 

®  =  1.27  x  2,083,000  =  2,650,000  webers. 

2.  Sectional  Area  of  Magnet  Frame.  —  According  to  formula 
(216)  and  Table  LXXVIIL,  §  82,  we  obtain  the  cross-section 
of  the  magnet  frame  : 

=  3.650.000  =  29  4      e  inches 

90,000 

The  axial  length  of  the  frame,  limited  by  the  length  of  the 
armature  core  on  the  one  hand  and  by  the  length  over  the 
armature  winding  on  the  other,  being  chosen  /p  =  5-J",  its 
thickness  is: 

29.4        _  . 

-  Y  =  o  inches. 

J  8 

3.  Polepteces  and  Magnet  Core.  —  The  bore  of  the  field  is  found 
by  summing  up  as  follows: 


DYNAMO-ELECTRIC  MACHINES. 


[§134 


Diameter  of  armature  core =  15.000  inches 

Winding 6  x  .088  =  .528       " 

Insulation  and  binding 2  x  .080  =  .160      " 

Clearance  (Table  LXI.) 2  x      A  =  -l87      " 

dr>  =  15.875  inches 


k- I 


Fig.  344. — Dimensions  of  Field  Magnet  Frame,  lo-KW  Single-Magnet  Type 

Generator. 

Making  the  width  at  the  centre  of  the  polepiece  one-half  the 
full  width,  and  rounding  off  the  total  height  of  the  machine,  we 
obtain  21  inches,  leaving  the  length  of  the  magnet  core; 

/m  =21  —  2X5  =  11  inches. 

The  distance  between  the  pole-tips  is  obtained  by  formula 
(150)  and  Table  LX.,  §  58,  as: 

/rp  =  5-5  X  (15!  -  15)  =  4-8  inches, 

while  the  assumed  percentage  of  polar  arc  corresponds  to  a 
pole  angle  of  fi  =  140°,  or  a  pole  space  angle  of  a  =  40°,  and 
therefore  furnishes: 

/'p  =  15!  x  sin  20°  =  5J  inches, 

the  larger  value  being  preferable  on  account  of  smaller  leak- 
age. 

The  distance  between  the  magnet  core  and  the  adjoining 
pole-tips  is  determined  by  Table  LXXX.,  §  83.  In  this,  the 
height  of  the  magnet-winding  for  a  28  square  inch  rectangular 
core  is  given  as  hm  =  2  inches;  allowing  y  clearance  we  ob- 


§134]      EXAMPLES  OF  GENERATOR   CALCULATION.          5J9 

tain  the  desired  distance,  and  making  the  width  of  the  pole- 
shoes  16  inches,  the  total  width  of  the  frame  becomes: 


5  +  2J-  +  16  =  23J  inches. 
Fig.  344  shows  the  field  magnet  frame  thus  dimensioned. 

C.    CALCULATION    OF    MAGNETIC    LEAKAGE. 

i.   Permeance  of   Gap-  Spaces.  —  The  actual  field-density,   by 
(142),  p.  204,  being 

yy  _  _          _  2,083,000 

^(i5  +  15*)  X  -2  X  .89  X^(5i  +  5l) 
—  I7)5°°  lines  per  square  inch, 

the  product  of  field  density  and  conductor  velocity  is 
3C"  X  z>c  =  I7,5°°  X  80  =  1,400,000; 


hence  the  permeance  of  the  gaps,  by  Table  LXVI.  and  formula 
(167),  page  226: 

X   ~  X  .89  x  5i 


1-325  X  (i5l  -  15)  1.16 

2.   Permeance  of  Stray  Paths. — The  area  of  the  pole-shoe  end 
surface,  5,  Fig.  164,  is,  according  to  Fig.  344: 


=  54.5  square  inches. 

This  into  (193)  gives  the  total  relative  permeance  of  the  waste 
field: 


<$  —      2ai  x  5 , 

3  — _*       I 


X  54-5  +51  X  M-  +  7     X 


M 


^ 


,   2t  X  51    ,    51  X  2 
"         ^^ 


'=  5-5  +  T7-3  +  i-3  +  2.0  =  26.1. 


520  DYNAMO-ELECTRIC  MACHINES.  [§134 

3.  Probable  Leakage  Factor.  —  From  (157),  p.  218: 
A  =  ,02.5  +  26.!  =   "8.6  =  j  266 

102.5  102.5 

This  being  smaller  than,  and  only  1.2  per  cent,  different 
from,  the  leakage  factor  taken  for  the  preliminary  calculation 
of  the  total  flux,  we  will  use  the  value  found  from  the  latter 
in  the  subsequent  calculations. 

d.    CALCULATION    OF    MAGNETIZING    FORCES. 

1.  Air  Gaps.  —  Length,  by  (166)  p.  224: 

l\  =  1.325  x  05-3-  —  J5)  =  r-16  inch- 
Area,  by  (141),  p.  204: 

Sg  =  15-5^  X  —  X  -89  x  5|  =  119  square  inches. 

Density,  by  (142),  p.  204: 

2,  08^,000 
3C    =  —  -  =  17,500  lines  per  square  inch. 

Magnetizing  force  required,  by  (228),  p.  339, 

<**g  =  •3I33  X  17,500  X  1.16  =  6360  ampere-turns. 

2.  Armature  Core.  —  Length  of  path,  by  (236),  p.  343: 

00°  -|-   20° 
l\  =  «i  X  TT  X  '-        6'Q<>      -  +  2-|  =  i4|  inches. 

Minimum  area  of  circuit,  by  (232),  p.  341: 

S&J  =  2  x  5-J  X  2-J  X  .90  =  26.5  square  inches. 
Maximum  area  of  circuit,  by  (233),  p.  341,  and  (234),  p.  342: 


Sa3  =  2  X  5i  X  2i  X   i  -  i   X  .9?  =  54-7  sq.  in. 

Average  specific  magnetizing  force,  by  (231),  p.  341: 


=  -  (29.5  X  7.1)  =  18.3  ampere-turns  per  inch. 


§134]      EXAMPLES  OF  GENERATOR   CALCULATION.          521 
Magnetizing  force  required,  by  (230),  p.  340: 

#/a  =  18.3  X  i4i  =  265  ampere-turns. 

3.   Magnet  Frame  (all  cast  steel). — Length  of  portion  with 
uniform  cross-section  (core  and  yokes) : 

^m  =  1 1  +  2  X  (5  -f  H)  —  26  inches. 
Area  of  magnet  core  and  yokes: 

Sm  =  5  X  5-J  =  29.4  square  inches. 
Density: 


(&"m  =  -—  -  =  90,000  lines  per  square  inch. 

Specific  magnetizing  force  (Table  LXXXVIIL,  or  Fig.  256): 
/  (®"m)  —  57  ampere-turns  per  inch. 

Mean   length  of  portion  with   varying   cross-section    (pole- 
pieces),  from  formula  (243) : 

l"v  =  2f  +  (  8±  +  7f  X  ~  )  -  5?V  =  l8  inches. 


Minimum  area: 

^Pl  =  5  X  5f  =  29.4  square  inches. 
Maximum  area: 

^Pa  =  M5l  X  ^  X  .78  +  2  x  ~  j  X  51  =  I2°   sq.    in. 
Average  specific  magnetizing  force,  by  formula  (241)  : 


-  =  30.8  ampere-turns  per  inch. 

Corresponding  flux  density,  by  Table  LXXXVIII.  : 

(B"p  =  78,000  lines  per  square  inch. 

Magnetizing   force    required    for   magnet    frame,     by    (238), 
P-  344: 

afm  =  57  X  26  +  30.8  x  18  =  2035  ampere-turns. 


522  DYNAMO-ELECTRIC  MACHINES.  [§134 

4.  Armature  Reaction.  —  According  to  Table  XCI.,  §  93,  the 
coefficient    of    armature-reaction   for  (B"p  =  80,000,    in    cast 
steel,  is  k^  =  1.25,  hence,  by  formula  (250),  the  magnetizing 
force  required  to  compensate  the  magnetizing  effect  of  the 
armature  winding: 

at,  =  1.25  x  *l?J<j4?  x  ^s  =  1870  ampere-turns. 

5.  Total  Magnetizing  Force  Required.  —  By  (227),  p.  339,  we 
have: 

AT  =  6360  -f  265  -f  2035  +  1870  =  10,530  ampere-turns. 

e.    CALCULATION    OF    MAGNET    WINDING. 

Temperature  increase  at  normal  load  not  to  exceed 
em  =  3°°  Centigrade.  Voltage  to  be  adjustable  between  225 
and  250,  in  steps  of  5  volts  each. 

i.  Winding  Proper  (for  E  =  250  volts).  —  Rounding  the  total 
magnetizing  force  to  11,000  ampere-turns,  formula  (287), 
§  99>  gives  the  number  of  series  turns: 

=  275. 


40 
The  length  of  the  mean  turn,  by  (290),  being 

'T  —  2  (Si  +  5)  +  2  X  TT  =  28  inches, 

the  total  length  of  the  series  field  wire  is  obtained,  by  for- 
mula (288)  p.  374: 


Formulae  (278)   and  (282)  give  the  radiating  surface  of  the 
magnet: 

SM3  =  2  X  ii  X  (51  +  5  +  2  X  n)  +  2  X  2  x  (28  -  si) 
=  466  square  inches, 

hence  by  (294)  the  resistance  required  for  the  specified  tem- 
perature increase: 


ij  -  -  --  =  .104  ohm, 
75        40"       i  +  .004  x  3° 


§134]  EXAMPLES  OF  GENERATOR  CALCULATION.  523 
and  therefore  by  (294)  the  specific  length  of  the  magnet-wire: 

\    —  _^li  =  6170  feet  per  ohm. 
.  104 

The  nearest  gauge  wire  is  No.  2  B.  &  S.,  which  is  too  incon- 
venient to  handle;  we  therefore  take  2  No.  7  B.  W.  G.  wires 
(.180"  -|-  .012"),  which  have  a  joint  specific  length  of  2  x 
3138.6  —  6237  feet  per  ohm.  Allowing  f  inch  for  the  core- 
flanges,  formula  (296)  gives,  for  this  wire,  an  effective  wind- 
ing depth  of 


2    X    .  IQ22 

=    3275    X  =    1. 


II  — 
Actual  resistance  of  magnet-winding  (from  wire  gauge  table) : 

rm  =  642  X  2°°°319  =  .1025  ohm  at  15.5-  C., 

or 

r'se  =  .1025  x  1.12  =  .115  ohm  at  45.5°  C. 

Weight  of  magnet  winding,  bare : 

wtm  =  2  x  642  x  .098  =  126  pounds; 
weight,  covered,  from  Table  XXVI.,  §  28: 

wt'm  —  1.0228  X  126  =  130  pounds. 

2.   Regulator  (see  diagrams,  §  100). — The  difference  of  5  volts 
between  each  of  the  five  steps  being 

-  =  2  per  cent,  of  the  full  load  output, 

the  shunt  coil  regulator  has  to  be  calculated  for  90,  92,  94,  96, 
and  98  per  cent,  of  the  maximum  E.  M.  F.,  the  resistances  of 
the  five  combinations,  therefore,  are: 

Resistance,  first     combination  —  |£  x  r'm  =    9        x  r'8e, 

"  second  "  =  $/-  x  r'K  =11.5     X  r'^, 

"  third  "  =  *£-  x  r'ae  =  15.67  X  r'M, 

"  fourth  "  =  .y.  x  ^'8e  =  24        x  r'M, 

fifth  "  =VxVM  =  49        X  r*», 


524  D  YNAMO-ELECTRIC  MA  CHINES.  [§  1 34 

By  the  proceeding  shown  in  §  100  we  then  obtain  the  follow- 
ing formulae  for  the  resistances  of  the  five  coils: 

_  (11.5  r'**  -  r\]  X  (9^'se  —  ^i) 

~ 


•5<e    -    n)    -    (9^'se    -    n) 
2.5    r'se 

=  45-5  >"8e-  8.2  ri;     '. (457) 

_  (15.67  r^  —  n)  X  (11.5  r'8e  —  rt) 
"  (15.67  r^  -  n)  -  (11.5  r'se  -  r,) 

160.2  r'sea  —  27.2  r'8e  r\  -\-  rf 

4-  I^y   r^ 

=  38.2  r'se  -  6.5  rt;    (458) 

rln  =  resistance  of  third  combination  minus  res.  of  leads 
=  15.67  r>m  -/-,;  (459) 

riv  =  res.  of  fourth  comb,  minus  res.  third  comb. 

=  (24  -  15.67)  r'se  =--  8.33  ^e;    .  • (460) 

rv   =  res.  of  fifth  comb,  minus  res.  fourth  comb. 

=  (49  -  24)  r'8e  =  25  r'se (461) 

These  formulae  apply  to  all  cases  in  which  a  total  regulation 
of  10  per  cent.,  in  five  steps  of  2  per  cent,  each,  is  desired. 
In  the  present  example,  the  resistance  of  the  series  winding, 
hot,  being  r'ge  —  .115  ohm,  and  the  resistance  of  the  leads 
rj  =  .01  ohm  (assuming  4  feet  of  4000  circular  mil  cable, 
carrying  10  per  cent,  of  the  maximum  current  output,  or  4  am- 
peres), we  have: 

•r\    —  45-5  X  .115  —  8.2    X  .01  —  5.15  ohms, 

rn  =  38.2  x  .115  -  6.2    x  .01  =  4.32      " 

>m=  T5-67  X  .115  -      -oi  —  1.79      " 

^iv  =    8.33  x  .115  =    .96     " 

rv   =  25  x  .115  =  2.88      " 

The  currents  flowing  in  the  various  coils,  at  the  different 
combinations,  are: 


§134]      EXAMPLES  OF  GENERATOR   CALCULATION,          525 
First  combination: 

/,    =  -JT^-T X.I/ 

ru  rm  "T  ri  rm  +  r\  ru 

4'32XI'79  X.IX40 


4.32  X  1-79  +  S..S5  X  i.79  +  S^S  X  4-32 

=  • — ^^ X  4  =  ^^  X  4  =  .8  ampere. 

7.73  +  9.22  +  22.35  39.3 

T*  rm  0.22 

11  ^  rlrm  +  rlrn-\-rllrmX  3^3  x  4  -  -95  amp. 

/m  "  *i  rn  +  ^m  +  rn  rm  X  '  *  7  =  ~^~f  X  4  =  2-3  amp. 
Second  combination: 


7m  —  -7—377 —  X  .08  7  —  ^Y  X  3.2  =  2.3  amperes. 

Third  combination: 

7m  =  .06  7  =  2.4  amperes. 

Fourth  combination: 

7m  =  7IV  =  .04  7  =  1.6  amperes. 

Fifth  combination: 

7m  =  7IV  =  7V  =  .02  7  =  .8  ampere. 

The  maximum   current   intensities   passing  through   the  five 

coils,  consequently,  are: 

7j    =  .8  amp.;  or,  in  general: 

7,    =.2  X  .i7=  .027, (462) 

7n   =  .95  amp.;  or,  in  general: 

7n   =  .3  X  .o87=  .0247, (463) 

7m  =  2.4  amp. ;  or,  in  general:     7m  =  .06  7,      (464) 

7IV  =  1.6  amp. ;  or,  in  general:     7IV  =  .04  7,      (465) 

7V    =  .8  amp. ;  or,  in  general:       7V   =  .02  7      (466) 

From  the  wire  gauge  table,  finally,  the  size  of  the  wire  suffi- 
cient to  carry  the  maximum  current,  and  the  length  and 
weight  of  the  same,  required  to  make  up  the  necessary  resist- 
ance", is  obtained: 


526 


D  YNAMO-ELECTRIC  MA  CHINES. 


[§134 


P. 

w>>; 

mi 

1  -^ 

8-0 

*&. 

+$••0 

COIL 
NUMBER. 

3J* 

$ 

.2SS 
8<£ 

32      O 

11* 

P 

JP 

IP 

0 

I 

.8 

No.  21  B.  &  S. 

810 

1012 

5.15 

400 

1.05 

II 

.95 

No.  20  B.  &  S. 

1021 

1073 

4.32 

427 

1.29 

III 

2.4 

No.  18  B.  W.  G. 

2401 

1000 

1.79 

414 

3.15 

IV 

1.6 

No.  18  B.  &  S. 

1624 

1015 

.96 

150 

.76 

V 

.8 

No.  21  B.  &  S. 

810 

1012 

2.88 

224 

.58 

/.    CALCULATION    OF    EFFICIENCIES. 

i.  Electrical  Efficiency. — The  electrical  efficiency  of  the  above 
dynamo,  by  formula  (351),  p.  405,  is: 

250  X  40 


250  X  40  4-  4o2  X  (.275  4-  .115) 


10,000 
10,624 


=  .943,  or  94.3$. 


2.  Commercial  Efficiency  and  Gross  Efficiency. — The  energy 
losses  due  to  hysteresis,  eddy  currents,  brush  contact,  and 
brush  friction  were  found  Ph  =  160,  PQ  =  4,  Pk  =  .315  X  746 
=  235,  and  Pt  =  .244  x  746  =  182  watts,  respectively;  as- 
suming that  journal  friction  and  air  resistance  cause  a  further 
energy  loss  of  500  watts,  the  commercial,  or  net  efficiency  of 
the  machine  will  be,  by  (359),  p.  361: 

10,000 


10,624  4-  160  4-  4  4-  235  4- 182  4-  500 
10,000 


11,705 


=  .855,  or  85.5  %. 


In  dividing  this  by  the  electrical  efficiency,  the  efficiency  of 
conversion,  or  the  gross  efficiency,  is  obtained  : 

%  =          =-9°7,  or  90.7*. 


3.    Weight  Efficiency.  —  The  weights  of  the  various  parts  of 
our  dynamos  are  as  follows: 


§135]      EXAMPLES  OF  GENERATOR   CALCULATION.          S27 

Armature : 

Core,  .292  cu.  ft.  of  sheet  iron,     .         .    140  Ibs. 
Winding  (§  134,  a,  7),  core  insulation, 

binding,  and  connecting  wires,  .     40  Ibs. 

Shaft,  spiders,  pulley,  keys,  and  bolts 

(estimated),       .....    100  Ibs. 
Commutator,  7"  dia.  X  3j"  length,        .     20  Ibs. 

Armature,  complete,      .  300  Ibs. 

Frame : 

Magnet  core  and  polepieces  (see  Fig. 
344  and  §  134,  c,  2),  (5  X  26  +  54.5) 
X  5-J  —  1084  cu.  ins.  of  cast  steel,    .   310  Ibs. 
Field  winding  (§  134,  c,    i),   core  insu- 
lation, flanges,  etc.,  ....    140  Ibs. 
Bedplate    (cast-iron),    bearings,    etc., 

(estimated),       .,      .  .,        .         .         .   250  Ibs. 

Frame,  complete,  .         .         .         .  700  Ibs. 

Fittings: 

Brushes,    holders,     and   brush-rocker, 

(estimated),       . ,       .         .         .         .20  Ibs. 

Field   regulator   (winding,   see  §    134, 

e,  2),     .      .         .         .         .         .         .15  Ibs. 

Switches,  cables,  etc.  (estimated),        .     15  Ibs. 

Fittings,  complete,         ....  50  Ibs. 

Hence  the  total  net  weight  of  the  machine,         .         1050  Ibs. 

The  useful  output  is  10  KW,  therefore  the  weight-efficiency, 
by  §  109: 

10,000        _  _ 

i=  9.5  watts  per  pound. 

135,  Calculation  of  a  Bipolar,  Single  Magnetic  Circuit, 
Smooth-Drum,  High-Speed  Shunt  Dynamo  : 

300  KW.    Upright  Horseshoe  Type.   Wrought-Iron 

Cores  and  Yoke,  Cast-Iron  Polepieces. 
500  Volts.    600  Amps.     400  Revs,  per  Min. 

a.    CALCULATION    OF    ARMATURE. 

i.  Length  of  Armature  Conductor. — For  this  machine,  since 
300  KW  is  a  large  output  for  a  bipolar  type,  we  take  the 
upper  limit  given  for  the  ratio  of  polar  embrace  of  smooth- 


528  DYNAMO-ELECTRIC  MACHINES.  [§135 

drum  armatures,  namely,  ftl  =-.75.  Hence,  by  Table  IV.,  p. 
50:  e  =  62.5  X  io~8  volt  per  bifurcation;  the  number  of  bifur- 
cations is  n'v  =  i.  The  best  conductor  velocity,  from  Table 
V.,  p.  52  :  vc  —  50  feet  per  second;  and  the  field  density,  from 
Table  VI.,  p.  54:  3C"  =  30,000  lines  per  square  inch.  'The 
total  E.  M.  F.  to  be  generated,  by  Table  VIII.  ,  p.  56: 
E'  —  1.025  x  500  =  512.5  volts. 
Consequently,  by  (26)  : 

^.      Xio* 


62.5  X  5°  X  30,000 

2.  Sectional  Area  of  Armature    Conductor,    and  Selection    of 
Wire.—Ky  (27),  p.  57: 

d£  —  300  x  600  =  180,000  circular  mils. 

Taking  3  cables  made  up  of  7  No.  13  B.  W.  G.  wires  having 
.095"  diameter  and  9025  circular  mils  area  each,  we  have  a 
total  actual  cross-section  of 

3  X  7  X  9025  =  189,525  circular  mils, 

the  excess  over  the  calculated  area  amply  allowing  for  the  dif- 
ference between  the  current  output  and  the  total  current 
generated  in  the  armature,  see  §  20. 

For  large  drum  armatures  cables  are  preferable  to  thick 
wires  or  copper  rods,  because  they  can  be  bent  much  easier, 
are  much  less  liable  to  wasteful  eddy  currents,  and,  since  air 
can  circulate  in  the  spaces  between  the  single  wires,  effect  a 
better  ventilation  of  the  armatures. 

In  accordance  with  §  24,  a,  a  single  covering  of  .007"  is 
selected  for  the  single  wires,  and  an  additional  double  coating 
of  .016"  is  chosen  for  each  cable  of  seven  wires,  making  the 
total  diameter  of  the  insulated  cable,  see  Fig.  345  : 

<*'a  =  3  X  (.095"  +  .007*)  +  .016'  =  .322  inch. 

3.  Diameter  of  Armature   Core.  — 
From  (30): 

d'&  =  230  x  —  =  28|  inches. 
400 

By  Table  IX.  : 

<4  =  -97  X  28  J  =  28  inches. 


§135]      EXAMPLES  OF  GENERATOR   CALCULATION.  529 

4.   Length  of  Armature  Core. — 
By  (37)  and  Table  XVII  ,  p.    73: 

28  x  n  X  (i  -  .08) 

nw  —  -  — -  =  252. 

.322 

By  (39),  p.  74,  and  Tables  XVIII.  and  XIX.  : 


.8  —  (.090  -j-  .O7o)_ 


,322 


By  (40),  p.  76: 


12  X  3  X 


7  


/547\ 

V  *•<*/  . 


=  37J  inches. 


252    X    2 

In  this  the  active  length  of  the  armature  conductor  has  been 
divided  by  1.04,  taking  into  consideration  the  lateral  spread  of 


Fig.  345. — Armature  Cable,  300- KW  Bipolar  Horseshoe-Type  Generator. 

the  field  in   the  axial  direction,    and   assuming  the   same   to 
amount  to  4  per  cent,  of  the  length  of  the  armature  core. 

5.   Arrangement  of  Armature    Winding. — 
By  (45)  p.  89,  and  Table  XXI: 


and 


-500  x  2 

(»c)m«   =       -— =    I0°- 


Two  values  of  nc  between  these  limits  can  be  obtained,  viz.  : 


«„  = 


_  252x2 


2    =    84, 


and 


252  X  2 

=      — •*-  3  =  56. 

•j 


For  the  latter  number  of  divisions,  however,  there  are  three 
conductors  per  commutator-bar,  and  since  the  armature  is  a 


53°  DYNAMO-ELECTRIC  MACHINES.  [§135 

drum,  there  would  be  i|-  turn  to  each  coil,  which  is  impossi- 
ble; therefore,  the  number  of  coils  employed: 

«0  =  84. 
By  (47),  P-  89,  then: 

252  X  2  .. 

-   2  X  84  X  3  ~ 

hence,  summary  of  armature  winding:  84  coils,  each  consisting 
of  1  turn  of  3  cables  made  up  of  7  No.  13  B.  W.  G.  wires. 


Ms  FIBRE 


84  DIVISIONS 

Fig.  346.  —  Arrangement  of  Armature  Winding,  3OO-KW  Bipolar  Horseshoe- 
Type  Generator. 

One  armature  division  containing  the  beginning  of  one  coil 
and  the  end  of  the  one  diametrically  opposite,  is  shown  in 
Fig.  346. 

6.     Weight  and  Resistance  of  Armature   Winding.  — 
By  (5°)i  P-  96: 

A  =  547  X  1  1  +  i-3  X     -T     =  1070  feet. 


1  +  i-3  X  J-JJT  J  = 


Here  the  original  value  of  Za,  without  reduction,  is  used,  in 
regard  of  the  fact  that,  in  a  cable,  due  to  the  helical  arrange- 
ment of  the  wires,  the  actual  length  of  each  strand  is  greater 
than  the  length  of  the  cable  itself,  and  under  the  assumption 
that  4  per  cent,  is  the.  proper  allowance  for  this  increase  in 
the  present  case. 
By  (58),  p.  101,  then: 

«//a  =  .00000303  x  189,525  x  1070  =  615  pounds. 
By  (59),  p.  102,  and  Table  XXVI.  : 

wt'&  =  1.031  x  615  =  634  pounds. 
From  (61),  p.  105: 

r&  =  -  —  X  1070  X  .001144  =  .0146  ohm,  at  15.5  °  C. 


§135]      EXAMPLES  OF  GENERATOR   CALCULATION.  53* 

7.    Radial  Depth,  Minimum  and  Maximum  Cross-  Section,  and 
Average  Magnetic  Density  of  Armature  Core.  — 
By  (123),  and  Table  XLVIIL,  p.  183: 


d.  =  i.55  x>-=  8  inches; 


see  also  Table  XLIX.,  p.  185;  therefore: 

j  28  _  8 

&*  =  -  (<4  —  4)  =  - 


=  10  inches, 


and  from  (234),  p.  342,  or  Fig.  347  : 

*'.  =  10  x  y 


i  =  13.4  inches. 

10 


Fig-  347- — Dimensions  of  Armature  Core,  3OO-KW  Bipolar  Horseshoe- 
Type  Generator. 

Hence  by  (232),  p.  341: 

^"a,  =  2  X  37J-  X  10  X  .95  =  712  square  inches, 
and  by  (233),  p.  341: 

^"a2  =  2  x  37i  X  13.4  X  .95  =  956  square  inches. 
From  (138),  p.  202 : 

-        6  x  512.5  X  io9 

1   X  84  X  4°°    ^  45>76°>000  W6berS; 

consequently: 

®"a,  =  =  64,200  lines  per  square  inch, 


S32  DYNAMO-ELECTRIC  MACHINES.  [§135 

and 

415,760,000 
($>  ^  =  —  —  —  ^  --  —  47,800  lines  per  square  inch. 

,  P-  34i,  and  from  Table  LXXXVIIL,  p.  336: 


*  \  -  ,  (47,8oo)  _  15.2  -f  9.1 

a)  =  —  — 

—  12.15  ampere-turns  per  inch, 
to  which  correspond  : 

(B"a  =  58,000  lines  per  square  inch. 

8.    Energy  Losses  in  Armature^  and  Temperature  Increase.  — 
By  (68),  p.  109: 

^  —  1.2  x  6oo2  X  .0146  =  6307  watts. 


^  =  -£—  =  6.67  cycles  per  second; 


(70)  P- 


18  X  n  x  371  X  10  X  .9  ,  .     £ 

M  —  -  Q  —  =  II-°5  cubic  feet; 

From  Table  XXIX.,  (&"a  =  58,000): 

77  =  20.92  watts  per  cubic  feet; 

From  XXXIII.,  (tf,  =  .010*): 

8  =  .0242  watt  per  cubic  feet. 
By  (73),  P-  112: 

Ph  =  20.92  x  6.67  x  11.05  =  1540  watts. 
By  (76),  p.  120: 

P^  =  .0242  X  6.672  x  11.05  —  12  watts. 
By  (65),  p.  107: 

A  =  6307  +  1540  +  12  =  7859  watts. 
From  Table  XXXV.,  p.  124: 

4  =  35  X  28  -f  2  x  .8  =   n£  inches. 

By  (78),  P.  124: 

SA=  (28  +  2  x  .8)  X  nr(37i+  I-8  x  Iri)  =  5412  s<^'  ins' 


§135]      EXAMPLES  OF  GENERATOR   CALCULATION.          533 
Ratio  of  pole  area  to  radiating  surface: 
30  X  7t  X  37t  X  .75  _ 


For  this  ratio  and  a  peripheral  velocity  of 

*  x  46°o°  -  51}  feet  per  second. 

Table  XXXVI.,  p.  127,  gives:  e'a  =  44.7°C.  ;  consequently 
by(8i): 

0a  =  44.7  X  0|  =  65°  Centigrade, 

and  the  resistance  of  the  armature,  when  hot,  is: 

r'a  =  .0146  X  (i  +  .004  X  65)  =  .0184  ohm,  at  80.5°  C. 

9.  Circumferential  Current  Density,  Safe  Capacity,  and  Run- 
ning Value  of  Armature;  Relative  Efficiency  of  Magnetic  Field.  — 
By  (84),  p.  131: 

84  X  2   X  300 
/c  =    —  8  --  ~          amperes  per  inch. 

Corresponding  increase  of  temperature,  from  Table 
XXXVII.  ,  p.  132:  0a  =  60°  to  80°  C,  which  checks  the 
above  result. 

By  (88),  p.  134,  and  Table  XXXVIII.  : 

P'  =  282  X  37i  X  .88  x  400  X  30,000  X  io~6  =  310,000  watts. 

By  (90),  p.  135: 

P>&  =  6i$'x  30,000  =  -0167  Watt  per  P°Und  °f  c°PPer>  at 

unit  field  density; 

this  also  verifies  the  calculation,  see  Table  XXXIX.,  p.  136. 
By  (i55),  P-  211  : 

^'p  ~  gi2*g  x°6oo  X  5°  ~  74:^  webers   per   watt,    at  unit 

velocity; 

by  Table  LXIL,  p.  212,  this  is  not  too  high. 


534  DYNAMO-ELECTRIC  MACHINES.  [§135 

10.    Torque,  Peripheral  Force,  and  Upward  Thrust  of  Arma- 
ture.— 
B7  (93),  P.  138: 

r  =  — ~2  x  600  X  168  X  45,760,000  =  5420  foot-pounds. 
By  (95),  p-  138: 

512.5  X  600 
'•  =  '7375  X  50  X  168  X  .88  =  30- 

By  (103),  p.  141: 

/t  =  ii  X  io-9  X  28  X  37i  X  (3Q,6oo2  -  29,400')  =  8321bs., 

under  the  assumption  that  the  density  of  the  upper  half  of  the 
field  is  2  per  cent,  above,  and  that  of  the  lower  half  2  per  cent, 
below,  the  average. 

b.    DIMENSIONING    OF    MAGNET    FRAME. 

1.  Total    Magnetic    Flux,    and    Sectional    Areas  of  Magnet 
Frame.  — 

By  (156),  p.  214,  and  Table  LXVIII.  : 

<£'  =  1.20  x  45,760,000  =  55,000,000  webers. 
By  (217),  p.  314,  wrought-iron  cores  and  yoke  being  used: 

i;  5,000,000 

Swl  =  ^ ? =  611  square  inches. 

90,000 

By  (216),  p.  313,  and  Table  LXXVI.,  the  minimum  section  of 
the  cast-iron  polepieces: 

=  55,000,000  =  11W)  e  .nches 

5O,OOO 

2.  Magnet  Cores. — Selecting  the  circular  form  for  the  cross- 
section  of  the  magnets,  their  diameter  is: 


dm  =  \/  61 1  x  -  =  28  inches. 

7t 

Length  of  cores,  from  Table  LXXXI.,  p.  319,  by  interpola- 
tion: 

/    =  35  inches. 


§135]      EXAMPLES  OF  GENERATOR   CALCULATION.          535 
Distance  apart,  from  Table  LXXXV.,  p.  323, 
c  =  16  inches. 

3.    Yoke. — Making  the  width  of  the  yoke,    parallel  to  the 
shaft,  equal  to  the  diameter  of  the  cores,  its  height  is  found: 

h   =  =  22  inches. 


SCALED  I NCH=1  FT. 

Fig.  348. — Dimensions  of  Field  Magnet  Frame,  soo-KW  Bipola* 
Horseshoe-Type  Generator. 

The  length  of  the  yoke  is  given  by  the  diameter  of  the  cores, 
and  by  their  distance  apart,  see  Fig.  348: 

/y  =  2  x  28  -}-  16  =  72  inches. 
4.  Polepieces. — The  bore  of  the  field  is  the  sum  of: 


536  DYNAMO-ELECTRIC  MACHINES.  [§135 

Diameter  of  armature  core,        =  28.000 

Winding 4  X.322",        =     1.288 

Insulation      and      binding, 

2  x   (.090"  4-  -070")        =      .320 
Clearance    (Table    LXI.    p. 

209) 2  xTy,     =    .375 

29.983  or,  say,  30  inches, 

Pole  distance,  by  (150),  p.  208,  and  Table  LX. . 
/'p  =  6  X  (30  -  28)  =  12  inches. 
Length  of  polepieces  equal  to  length  of  armature  core,  or: 

/p  =  37J  inches. 
Height  of  polepieces,  same  as  bore: 

hv  =  30  inches. 
Thickness  in  centre,  requiring  half  of  the  full  area: 

1 100 


2  X  37i 
Height  of  pole-tips: 


=  14.7,  say  15  inches. 


1/30—  A/308  -  i22    ]  =  I]  inch. 

Height  of  zinc  blocks,  from  Table  LXX.,  p.  301: 
hz  =  11  inches. 

C.    CALCULATION    OF    MAGNETIC    LEAKAGE. 

i.   Permeance  of  Gap-  Spaces.  — 

OC"  X  z>c  =  3°>000  X  5°  =  i,500>000» 
therefore,  by  (167),  p.  226,  and  Table  LXVI.  : 


_ 


1-35   X  (30  -  28)  2.7 

2.   Permeance  by  Stray  Paths.  — 

By  (178),  p.  232: 

_        28  X  7t  X  35        _  4  1 
*>  ~  2  x  16  +  1.5  X  28  -    **l 


§135]      EXAMPLES  OF  GENERATOR   CALCULATION.  537 

By  (188),  p.  239: 

7  X  [37i  X  (28  +  15)  +  850] 
3,  = =  56, 

2    X    II 

the  portion  of  the  bed  plate  opposite  'one  polepiece  being  esti- 
mated to  have  a  surface  of  S  =  850  square  inches.  The  pro- 
jecting area  of  the  polepiece,  see  Fig.  349,  is 


K—  -- 16 *, 


Fig-  349- — Top  View  of  Polepiece,  300  KW  Bipolar  Horseshoe-Type 
Generator. 

S3  =  16  x  37|-  -f  i62  X  -  -  28*  -  =  386  square  inches, 
hence  by  (199),  p.  245: 

«•  _.  386 37j  X  30 


35 


=  ii  +  7-4  =  18.4, 


2  X  35  +  (30  +  22)  X  - 


3.   Probable  Leakage  Factor.  — 
By  (157),  p.  218: 


.4  _     652  _ 
" 


,     .  536  +  41.6  +  56 

~^~ 
Total  flux: 

<£'  =  1.215  x  45,760,000  =  55,700,000  webers. 

d.    CALCULATION    OF    MAGNETIZING    FORCES. 

i.   Air  Gaps.  — 
Length,  by  (166),  p.  224: 

l\  =  1.35  x  (30  —  28)  =  2.7  inches. 


538  DYNAMO-ELECTRIC  MACHINES.  [§135 

Area,  by  (141),  p.  204: 

Sg  =  29  x  -  X  .88  X  37 J  =  1500  square  inches. 
Density,  by  (142),  p.  204: 

3C"  =  — =  30,500  lines  per  square  inch. 

Magnetizing  force  required,  by  (228),  p.  339: 

afe  =  -3I33  X  30,500  x  2.7  =  25,800  ampere-turns. 
2.  Armature  Core. — 
Length,  by  (236),  p.  343,  see  Fig.  350: 

T  I  7-1  ° 

l\  =  18  x  n  X    — P-  -f  10  =  27.85  inches. 


Fig.  350.—  Flux  Path  in  Armature,  aoo-KW  Bipolar,  Horseshoe-Type 
Generator. 

Minimum  area,  by  (232),  p.  341  : 

•Sk,  =  2  X  37|  X  10  x  .95  =  712  square  inches. 
Maximum  area,  by  (233),  p.  341  and  (234),  p.  342: 

•Saa  =  2  X  37i  X  13.4  X  95  =  956  square  inches. 
Average  specific  magnetizing  force,  by  (231),  p.  341  : 
/(64,*oo)+/(47,8oo) 


Magnetizing  force  required,  by  (230),  p.  340: 
at&  —  12.15  X  27.85  =  340  ampere-turns. 


§135]      EXAMPLES  OF  GENERATOR   CALCULATION.  539 

3.  Wr -ought-iron  Portion  of  Frame  (Cores  and  Yoke). — 
Length: 

''wj.  =  2  X  35  +  22  +  44  =  136  inches. 
Area: 

Svi  =  28"  —  =  6i5f  square  inches. 
4 

Density: 
(B*wi  =  ">7     > —  _  20)000  iines  per  square  inch. 

Specific  magnetizing  force: 

/(®"w.i.)  =  5°-7  ampere-turns  per  inch. 
Magnetizing  force  required: 

afwL  =  50.7  x  136  =  6900  ampere-turns. 

4.  Cast-iron  Portion  of  Frame  (Polepieces). — 
Length,  by  (243),  page  348: 

l\.\.  —  35  +  2  =  37  inches. 
Minimum  area  (at  center): 

•S"c.i.i  =  15  X  37i  =  562i  square  inches. 
Corresponding  maximum  density: 

(B"ci >x  —  £ 5g>700>oc  3  _  49)500  iines  per  SqUare  inch. 

Maximum  area  (at  poleface): 

•SaL,  =   (  30  X  w  X  y|^-  +  2  X  ij  j  X  37i  =  MOO  sq.  ins. 

Corresponding  minimum  density  : 

45,760,000 
&"ci2  =  3£L^_^__      =  32,700  lines  per  square  inch. 

Average  specific  magnetizing  force: 

/«*"„.)  =  \  [/(49,5oo)  +/(32)7oo)]  -  I55+57'6 

=  106.3  ampere-turns  per  inch. 
Corresponding  average  density: 

&"ci  =  43,500  lines  per  square  inch. 


540  DYNAMO-ELECTRIC  MACHINES.  [§135 

Magnetizing  force  required: 

atci  —  106.3  X  37  =  3930  ampere-turns. 

5.   Armature  Reaction.  — 
By  (250),  p.  352,  and  Table  XCL: 


atv  =  1.73  X  -         X  =  5700  ampere-turns. 

2  IOO 

6.    Total  Magnetizing  Force  Required.  — 

B7  (227),  p.  339: 

^T7  =  25,800  -f  340  -f  6900  -f  3930  +  5700 
=  41,670  ampere-turns. 

e.    CALCULATION    OF    MAGNET    WINDING. 

Shunt  winding  to  be  figured  for  a  temperature  increase  of 
15°  C.  Regulating  resistance  to  be  adjusted  fora  maximum 
voltage  of  540,  and  a  minimum  voltage  of  450. 

i.  Percentage  of  Regulating  Resistance  at  Normal  Load.  —  The 
maximum  .output  of  540  volts  requires  a  total  E.  M.  F.  of 

512.5  -f  40  =  552.5  volts, 

which  is  7.  8.  per  cent,  in  excess  of  the  total  E.  M.  F.  gen- 
erated at  normal  output;  for  the  maximum  voltage,  therefore, 
1.078  times  the  normal  flux  must  be  produced.  The  magnet- 
izing forces  required  for  this  increased  flux  are  : 

Air  gaps: 

at'g  =  .3133  x  (30,500  X  1.078)  x  2.7  =  27,800  ampere-feurns. 
Armature  core: 

at'*  =  /(58>o°o  X  1.078)  X  27.85  =  14.2  X  27.85 
=  400  ampere  turns. 

Wrought  iron: 

<tf'w.L  =/(90,ooo  X  1.078)  X   136  =  73-6  X  136 

=  10,000  ampere  turns. 
Cast  iron  : 

^'c.i.  =  /(43,5oo  X  1.078)  x  37  =  M4  X  37 
=  5320  ampere-turns. 

Armature  reaction: 

at'T  =  1.77  x  -  -  X  -~—  =  5820  ampere-turns. 


§135]        EXAMPLES   OF  GENERATOR   CALCULATION.         54* 

The  total  magnetizing  force  needed  for  maximum  output, 
consequently,  is: 

AT  =  27,820  -|-  4°°  +  10,000  -{-  5320  -|-  5820  =  49,340  am- 
pere-turns. 

This  surpasses  the  nomal  excitation  by 

xoox   (49,340-  41,670)  =  ^ 

41,670 

that  is  to  say,  the  extra-resistance  in  circuit  at  normal  output 
must  be  18  per  cent,  of  the  magnet  resistance,  in  order  to  pro- 
duce the  maximum  voltage  of  540  with  the  regulating  resist- 
ance cut  out. 

2.   Magnet  Winding  (for  500  Volts}.  —  The  mean  length  of  one 
turn,  by  (292),  p.  375,  and  Table  XCIV.,  being 

4  =  3-43  X  28  =  96  inches, 

the  specific  length  of  the  required  magnet  wire  is  directly 
obtained  by  (319),  p.  385: 


The  nearest  gauge  wires  are  No.  13  B.  W.  G.  (.095"  -f-  .010") 
and  No.  n  B.  &  S.  (091*  -j-  -OIO")>  having  874  and  798  feet  per 
ohm,  respectively.  The  former  being  about  5  percent,  above, 
and  the  latter  about  4  per  cent,  below,  the  required  figure, 
the  regulating  resistance  in  circuit  at  full  load,  when  No.  13 
B.  W.  G.  were  used,  would  be  about  23  per  cent.,  and  for  No. 
ii  B.  &  S.  would  be  about  14  per  cent,  of  the  magnet  resist- 
ance. In  order  to  obtain  the  exact  amount  of  regulating 
resistance  desired,  the  two  sizes  must  be  suitably  combined. 
Taking  e^qual  weights  of  each,  the  resultant  specific  length  is: 


=  -°419  X4  -       =  834  feet  per 


where  .0419  and  .0503  are  the  resistances  per  pound  of  the  two 
wires.  This  specific  length  being  practically  the  same  as  found 
above,  the  winding  calculated  on  its  basis  will,  in  fact,  make 
rx  =  18,  which  therefore  is  to  be  used  in  the  formulae. 


542  DYNAMO-ELECTRIC  MACHINES.  [§  135 

The  height  of  the  winding  space  derived  from  the  above 
value  of  /T  is: 

Am=  -  -  --  28  —  2  J  inches, 

and  this  into  formula  (277),  page  369,  gives  the  radiating   sur- 
face of  the  magnets: 

Sx  =  (28  +  2  x  z\  )  n  X  2  (35  —  2-|)  =  6730  square  inches, 
an  allowance  in  length  of  2^  inches  per  core  being  made  for 
flanges,  spools,  and  insulation. 
Hence  by  (312),  p.  383: 

p>*  —    ^f  X  6730  x  1.18  =  1590  watts, 

by  (314),  p.  384: 

^sh  =  41,670  Xjoo  =  shunt_turns. 

J59° 
and  by  (315),  p.  384: 

Ah  =  I3>I°i°2X96^  104,800  feet. 
consequently, 

^sh  =  I01*  °°  =  125.5  ohms,  resistance  of  winding,  cold 
834 

(15-5°  C.); 

and  by  (318),  p.  385: 

T-'sn    =  125.5  X   (i  +  .004  x   15)  =  133  ohms,  resistance 
of  winding,  warm  (30.5°  C). 

By  (317),  P.  384: 

r"sb   =  J33  X  1.18  =  157  ohms,  resistance  of  entire  shunt 

circuit,  at  normal  load; 
therefore: 

/sh    =  -  —  =  3.18  amperes,  shunt  current,  at  normal  load. 

Dividing  the  magnet  resistance  (cold)  by  the  average  resist- 
ance per  pound  of  the  two  sizes  used  (equal  weights  being 
taken),  we  obtain  the  weight  of  the  shunt  winding: 

1^_5  -  _  2720  pounds,  bare  wire, 


~  (.0419 


§135]     EXAMPLES  OF  GENERATOR   CALCULATION.  543 

or,  see  Table  XXVI.,  p.  103: 

wt'sh  =  1.03  x  2720  =  2800  pounds,  covered  wire. 

By  (325)>  P-  388,  we  receive: 

06 
otfsh  =  3i-3  X  io-6  X  13,100  x   —   X  834  =  2730  Ibs., 

which  checks  the  above  figure. 
Formula  (257),  p.  361,  gives: 


X  .04.800  X     '°95 


(' 


—  2.2  inches. 

Allowing.  3  inch  for  insulation  between  the  layers,  thickness 
and  insulation  of  bobbins,  and  clearance,  the  total  height  of  the 
magnet  winding  becomes  hm  =  2.  2  -|-  .3  =  2.5  inches,  which 
is  the  same  as  used  in  calculating  the  winding.  There  are, 
consequently,  no  errors  to  be  corrected,  and  the  final  result  of 
the  winding  calculation  is: 

14:00  Ibs.  (covered)  of  No.  13  B.W.G.  wire  (.095"  +  .010") 
and 

1400  Ibs.  (covered)  of  No.  11  B.  &  S.  wire  (.091"  -f  .010*), 

each  wound  in  4  spools  of  350  pounds,  two  spools  of  each  size 
to  be  placed  on  each  magnet,  see  Fig.  348.  Total  weight  of 
magnet  wire,  2800  pounds. 

3.  Shunt  Field  Regulator.  —  The  amount  of  regulating  resist- 
ance in  circuit  at  normal  load  required  for  the  maximum  volt- 
age in  the  preceding  was  found  to  be  18  per  cent,  of  the 
magnet  resistance.  In  order  to  reduce  the  voltage  from  the 
normal  amount  to  the  minimum  of  450,  the  total  E.  M.  F.  gen- 
erated must  be  decreased  from  512.5  to  512.5  —  50  =  462.5 
volts,  or  by  9f  per  cent.;  hence  the  minimum  flux  is  .9025  of 
the  normal  flux,  and  the  magnetizing  forces  for  the  minimum 
voltage  are: 


544  DYNAMO-ELECTRIC  MACHINES.  [§  135 

Air  gaps : 

at"g  =  .3133    X    (30,500     x    .9025)    x    2.65*    =    22,800 
ampere-turns. 

Armature  core: 

at\  =7(58,000  x  .9025)    X  27.85  =  10.3  x  27.85  —  270 
ampere-turns. 

Wrought  iron: 

at"w.i.  =7(90,000  X  .9025)  X  136  =  33-2  X  136   =  4520 
ampere-turns. 

Cast  iron : 

<tf*c.L  =/(43»5°°   X  .9025)    X    37    =   86.8    X    37  =   3210 
ampere-turns. 

Armature  reaction: 

at"r  =  1.7    x    — —  X  ^~  —  5600  ampere-turns. 

2  I5O 

The  total  excitation  required  for  minimum  voltage  is  the 
sum  of  the  above  magnetizing  forces: 

AT'  =  22,800  -f  270  -j-  4520  +  3210  -f  5600  =:  36,400 
ampere-turns. 

This  minimum  excitation  being 

xoo  X  (41,670--  36,400)  =  nt 

41,670 

smaller  than  the  normal  excitation,  the  normal  resistance  of 
the  shunt  circuit,  in  order  to  effect  the  corresponding  increase 
in  the  exciting  current,  must  be  increased  by  12.7  per  cent.,  or 
the  magnet  resistance  by  1.18  x  12.7  =  15  per  cent. 

The  total  resistance  of  the  regulator,  therefore,  by  formula 
(330>  P-  393,  is: 

rT  =  (.18  +  .15)  X  r'8h  =  .33  +  133  =  44  ohms. 

By  (332),  P.  393: 

-  >   .      (/*h)max  =     ~  =  4.o6  amperes. 


*  For  the  minimum  density  the  product  3C'  X  Vc  being  1,500,000  X  .9025 
=  1,353,750,  Table  LXVI.  gives  a  coefficient  of  field-deflection  k^  =  1.325, 
which  makes  the  length  of  the  magnetic  circuit  in  the  gaps  /"g  =  1.325  X  (30 
—  28)  =  2.65  inches. 


§135]      EXAMPLES  OF  GENERATOR   CALCULATION.          545 

%  (333),  P-  393  : 

(7sh)min   =  -  -  =  2.54  amperes. 

Supposing  that  the  regulator  is  to  have  60  contact-steps,  so 
as  to  give  an  average  regulation  of  ij  volt  per  step,  the  resist- 
ance of  each  coil  of  the  rheostat  will  be 

£=.733  ohm; 

and  if  iron  wire  at  6500  circular  mils  per  ampere  is  employed, 
the  area  of  the  wires  for  the  various  coils  ranges  between  4.06 
X  6500  =  26,390  and  2.54  x  6500  =  16,510  circular  mils.  The 
data  for  the  gauge  numbers  lying  between  these  limits  are: 

GAUGE  DIAMETER    SECTIONAL  AREA    CARRYING  CAPACITY,  AMPS. 

NUMBER.  (inch).  (Cir.  Mils),  v  (6500  Cir.  Mils  p.  A.) 

No.  6.  B.  &S 162 26,251 4.04 

No.  9B.  W.  G 148 21,904 3.38 

N0..7B.&S 144......     20,817 3.21 

No.  10  B.  W.  G 134 17,956 2.76 

No.8B.&S 1285 16,510 2.54 

Inserting  the  above  values  of  the  current  capacities  into 
formula  (335),  p.  394,  we  obtain: 

4.06   —  4.04 


4.06   -   2.54 

4.o6   --  3-38 
4.06   --  2.54 


X    60   =  i  , 
X    60   =   27 


_4.o6   -  _32_i         6 
"«  -  4.06   --   2.54    ' 

4.06   —   2.76 

"••  =  irf-i:"TM   X   *>==5i, 
and 

^  =  fJ*J-_!J4   X6o  =  6o; 

4.06      --      2.54 

from  which  follows  that  coils  i  to  26  are  to  consist  of  No.  6 
B.  &  S.  wire,  of  which  about  300  feet  are  needed  for  the 
required  resistance  of  .733  ohm;  that  coils  27  to  32  are  to  be 
of  No.  9  B.  W.  G.,  length  per  coil  about .250  feet;  coils  33  to  50 
of  No.  7  B.  &  S.,  length  about  240  feet;  coils  51  to  59  of  No.  10 


546  DYNAMO-ELECTRIC  MACHINES.  [§135 

B.  W.  G.,  length  about  205  feet;  and  coil  60  of  No.  8  B.  &  S. 
wire,  about  190  feet  in  length. 

/.    CALCULATION    OF    EFFICIENCIES. 

1.  Electrical  Efficiency.  — 

By  (352)>  p-  406: 

500  .X  600  _  300,000 

V*  =  500  X  600  +  603.  i82  X  .0184  +  3.i82  X    157   "  308,280 
=  -975,  or  97.5  fa 

2.  Commercial  Efficiency  and  Gross  Efficiency.  —  The   energy 
lost  by  hysteresis  and  eddy  currents  was  found  Ph  -j-  P&  =  1552 
watts;  energy  losses  by  commutation  and  friction  estimated  at 
12,000  watts;  hence  the  commercial  efficiency,  by  (360),  p.  407  : 

300,000  300,000  ~rt  _ 

*  =  308,280  +  I55*  +  .2,ooo  «  3-783*    :=  ^'  ^  M'8  *'' 
and  the  gross  efficiency: 


3.    Weight  Efficiency.  —  The  net  weight  of  the  machine  is  esti- 
mated as  follows: 
Armature: 

Core,  11.05  cu.  ft.  of  wrought  iron,     5,300  Ibs. 

Winding,  insulation,  binding,  etc.,  .        700    " 

Shaft,  commutator,  pulley,  etc.,       .     3,000 


<.  i 


Armature,  complete,          ....         9,000  Ibs. 
Frame : 

Magnet  cores,  28"  —  X  70  = 
4 

43,100  cu.  ins.  of  wrought  iron,         12,075  Ibs. 
Keeper,  28  X  22    x   72   =  44,35° 

cu.  ins.  of  wrought  iron         -.  12,325    " 

Polepieces,  about 

(18  X  30  X  37i)  X  2  =  40,500 

cu.  ins.  of  cast  iron         .         .          10,600    " 
Field    winding,     core    insulation, 

spools,  flanges,  etc.,  .  3, ooo    " 

Bedplate,    bearings,    zinc   blocks, 

etc.,     .         .         .         .         .  10,000    ll 

Frame,  complete,    .      '   .         .         ^         .*       48,000  Ibs. 


§136]       EXAMPLES  OF  GENERATOR    CALCULATION.         547 

Fittings: 

Brushes,      holders,      and  brush 

rocker,        .        ...     ,,,  .         .         400  Ibs. 

Switches,  cables,  etc.,     .  .         .          300    " 


Fittings,  complete,   .         .     ' "-.. '       .      / '.  -J     •    700  Ibs. 


Total  net  weight  of  dynamo,  .         .       57,700  Ibs. 

Hence,  the  weight  efficiency: 

3°0>00°  =  5.2  watts  per  Ib. 
57>7°o 

136.  Calculation  of  a  Bipolar,  Single  Magnetic  Circuit, 
Smooth-Drum,  High-Speed  Compound  Dynamo: 

300  KW.    Upright  Horseshoe  Type.    Wrought-Iron 

Cores  and  Yoke.    Cast-Iron  Polepieces. 
500  Yolts.     600  Amps.     400  Revs,  per  Min, 

The  armature  and  field  frame  calculated  in  §  135  are  given; 
the  machine  is  to  be  overcompounded  for  a  line  loss  of  5  per 
cent.  ;  temperature  of  magnet  winding  to  rise  22%°  C.  ;  extra- 
resistance  in  shunt  circuit  to  be  not  less  than  18  per  cent,  at 
normal  load. 

a.    CALCULATION    OF    MAGNETIZING    FORCES. 

T.  Determination  of  Number  of  Shunt  Ampere- Turns. — Use- 
ful flux  required  on  open  circuit: 


hence  by  §  104: 


44,700,000 
-    -3I33    X     -          --  X  1.325  (30  -  28) 


—  -3X33  X  29,800  x  2.65  =  24,700  ampere-turns. 


=  10.3  x  27.85  =  290  ampere-turns. 


54^  DYNAMO-ELECTRIC  MACHINES.  [§  136 

X   I36=/  (88,2oo)  x   I36 


—  46.4  X  136  =  6310  ampere-turns. 
2I     X 


/44,  7£o,ooo 

V  "~HOT- 


X37 


=  99.6  x  37  —  3680  ampere-turns. 

ATsh  =  ATQ  =  24,700  +  290  -f  6310  +  3680 
=  34,980  ampere-turns. 

2.   Determination  of  Number  of  Series  Amp  ere-  Turns.  —  Total 
E.  M.  F.  at  normal  output,  by  (333),  p.  393: 

E'  —  1.05  x  500  -f-  1.25  X  603  x  .0184  =  539  volts; 
and  therefore: 


48,200,000 

<*'g  •-=  -3133  x  2-~j5; —  x  1.35  (30  -  28) 

=  '3*33  X  32,100  x  2.7  =  27,100  ampere-turns. 


=  13.7  x  27.85  =  380  ampere-turns. 


./1.  2  15  X   48,  200, 

'W.L=//  -      ^5775" 


,000\ 

)  X  I36  =/  (95,2oo)  X  136 


=  67.8  x  136  =  9220  ampere-turns. 


2x56^.5 
=  123.9  x  37  =  4580  ampere-turns. 

a/r    =  1.76  x    4  X    °3   X  ^|*-  =  5820  ampere-turns. 

2  I  oO 

AT  =  27,100  +  380  -j-  9220  -f  4580  -\-  5820 

=  47,100  ampere-turns. 
Consequently,  by  (339),  p.  397: 

ioo  -  34,980  =  12,120  ampere-turns. 


§136]         EXAMPLES  OF  GENERATOR   CALCULATION.        549 
b.    CALCULATION    OF    MAGNET    WINDING. 

i.   Series  Winding.  — 

By  (338),  P.  396: 


=  1,267,000  circular  mils. 

Taking  5  cables  of  19  No.  9  B.  &  S.  wires  each,  the  actual 
area  is: 

5  Xi9  X  13,094  =  1,243,930  circular  mils. 

The  number  of  turns  required  is: 

N^  =  *2'*       =  20,  or  10  turns  per  core; 
hence  the  series  field  resistance,  at  15.5°  C.,  by  (344),  p.  400: 


and  the  weight: 

wtse  =  20  x  -'  X  (5  X  19  X  13,094)  =  6031bs.,  bare  wire; 
or, 

w/'ae  =  1.028  x  603  =  620  Ibs.,  covered  wire. 

2.  Shunt  Winding.  —  The  potential  across  the  shunt  field 
being  1.05  x  500  =  525  volts,  the  specific  length  of  the  shunt 
wire,  for  18  percent,  extra-resistance,  and  22^°  C.  rise  in  tem- 
perature, is,  by  (319),  p.  385: 

X  ^  X   1.18  X  (i  +  .004  X  22')  , 

=  687  feet  per  ohm. 

The  two  nearest  gauge  numbers  are  No.  n  B.  &  S.  (798 
feet  per  ohm)  and  No.  14  B.  W.  G.  (667  feet  per  ohm);  taking 
two  parts,  by  weight,  of  No.  14  B.  W.  G.  to  one  part  of  No.  n 
B.  &  S.,  we  obtain: 

=  .0503  X  79«  +  «X.  07.8  X  667  =          ^ 

•0503   +    2    X    .0718 

which   is  a  trifle  more  than  2  per  cent,   in  excess  of  the  re- 
quired specific  length.     By  increasing  the  percentage  of  extra 


55°  DYNAMO-ELECTRIC  MACHINES,  [§  136 

resistance  in  the  same  ratio,  that  is,  by  making  r^  =  20  per 
cent.,  formula  (319)  will  give  the  specific  length  actually  pos- 
sessed by  the  combination  of  shunt  wires  selected.     Hence: 
by  (346),  p.  400  : 

22-1° 

^sh  =  —  §-  X  6730  —  6oo2  x  .00135  X  (i  +  .004  X  22j°) 
=  2020  —  530  =  1490  watts; 

by  (3"),  P-  383: 

^sh    =  i49°  X  1.20  =  1788  watts; 

by  (3H),  P-  384: 

25  =  10,270  turns;  ,          .' 


Zsh    =  10,270  x  —  =  82,160  feet; 


by  (315),  P- 

sh    =  10, 
Weight: 
***  =  82,160  x  2X   '  -  =  1825  Ibs.,  bare  wire, 

o 

wt'fr  =  1.035  X  1825  =  1890  Ibs.,  covered  wire; 

Resistance: 
rah     =  —  !  --  =  117  ohms,  resistance  of  shunt  winding,  15.5°  C.; 

by  (318),  p.  385: 

r'ah    =  117  X  (i  +  -°°4  X  22^)   =  127.5  ohms,  resistance  of 
shunt  winding,  38°  C.  ; 

by  (317),  P-  384^ 

r'&    —   I27-5   X    1.20  =  153  ohms,   resistance  of  entire  shunt 
circuit,  normal  load. 

•'•     Sab=         —  3.43  amperes,  shunt  current,  normal  load. 

3.   Arrangement  of  Winding  on  Cores.  — 

Total  weight  of  series  winding:        .  wt'9G  =    620  Ibs. 
Total  weight  of  shunt  winding:        .   o//'sh  =  1890  Ibs. 

Total  weight  of  magnet  winding:     .         .        2510  Ibs. 


§136]        EXAMPLES   OF   GENERATOR   CALCULATION.         551 

The  weight  of  the  series  wire  being  just  about  one-quarter  of 
the  total  weight,  the  winding  is  with  advantage  placed  Upon 
8  spools,  4  per  core,  the  lower  one  of  each  being  used 
for  the  series  wire,  one  of  the  upper  three  being  wound  with 
No.  u  B.  &  S.,  and  the  remaining  two  with  No.  14  B.  W.  G. 
wire;  weight  of  wire  per  series  spool,  310  pounds,  per  shunt 
spool,  315  pounds. 

Each  series  spool  has  5  X  TO  =  50  cables  which  are  arranged 
in  4  layers,  two  of  which  contain  12,  and  two  13  cables.  The 
diameter  of  each  series  cable,  consisting  of  19  No.  9  B.  &  S. 
wires,  is  5  X  (.  1144"  -f-  .010")  =  .622  inch,  hence  the  winding 
depth  in  the  series  spools,  4  X  .622"  =  2.488  inches,  and  the 
length  of  one  layer  (13  cables)  =  13  X  .622*  =  8.086  inches. 
Since  the  available  height  of  each  spool  is 


lls:  Scinches, 

by  this  arrangement  the  spool  will  be  just  filled. 

In  the  shunt  bobbins  the  total  10,270  turns  are  divided  in 
the  ratio  of  the  quantities  used  and  of  the  specific  lengths 
(feet  per  pound)  of  the  two  sizes  of  wire,  /.  <?.,  in  the  ratio  of 
2  x  48  :  40,1;  hence  there  are 

10,270  x  -  ^  --  =  7240  turns  of  No.  14  B.  W.  G. 

2    X    48    -f-  4°-  I 

and 

10,270  x  -  -  =  3030  turns  of  No.  11  B.  &  S. 

2  x  4°  -r  4°.  i 

Each  No.  14  B.  W.  G.  spool,  therefore,  contains 


-  =  1810  turns, 

4 

and,  the  number  of  turns  per  layer  being 

8.125 


.083  -f-  .010 

has  a  net  winding  depth  of 
1810 


-87, 


X  .093"  =  1.95  inch. 


55 2  DYNAMO-ELECTRIC  MACHINES.  [§137 

Each  of  the  No.  n  B.  &  S.  spools  has 

=  1515  turns;  %'^      . 

the  number  of  turns  per  layer  is: 

8''25     -=80, 

.091  -|-  .010 
and  consequently,  the  net  winding  depth: 

'-I15  x  .101' =  1.92  inch, 
oo 

Actual  magnetizing  force  at  full  load : 

AMPERE-TURNS. 

Series  magnetizing  force,  AT^  —          20  x  600    =  12,000 
Shunt  magnetizing  force,  AT^  =  10,270  x  3,43  —  35,226 

Total  magnetizing  force,       .         .         .         .     4:7,226 

137.  Calculation  of  a  Bipolar,  Double  Magnetic  Circuit, 
Toothed-Ring,  Low-Speed  Compound  Dynamo: 

50  KW.    Double  Magnet  Type.   Wrought-Iron  Cores. 

Cast-Iron  Yokes  and  Polepieces. 
125Tolts.    400  Amps.    200  Keys,  per  Min. 

a.    CALCULATION    OF    ARMATURE. 

1.  Length  of  Armature  Conductor. — For  ftl  =  .70  (a  =  27°), 
Table  IV.,   p.    50,   gives  e  =  60  x  io~8  volt  per  foot;   from 
Table  V.,  p.  52,  vc  =  32  feet  per  second;  from  Table  VI.,   p. 
54,  3C"  =  20,000  lines  per  square  inch;  and  from  Table  VIII., 
p.  56,  E'  —  1.064  X  125  =  133  volts;  hence  by  (26),  p.  55: 

Za  =  ,      I33  X  IQ8 =  346  feet. 

60  X  32  X  20,000 

2.  Sectional   Area   of  Armature    Conductor,    and   Selection  of 
Wire.— 

By  (27),  p.  57: 

tfa2  =  300  x  400  =  120,000  circular  mils. 

For  20  No.    14   B.  W.    G.   wires  (.083*  -f-  .016"),  the  actual 

area  is: 

20  x  6889  =  137,980  circular  mils. 


§137]       EXAMPLES  OF  GENERATOR   CALCULATION.         553 

The  subdivision  of  the  armature  conductor  into  a  large  num- 
ber of  wires  has  the  particular  advantage  in  toothed  arma- 
tures, that  by  a  simple  regrouping  of  the  wires,  the  same  slot 
will  answer  for  a  number  of  different  voltages.  Thus,  in  the 
present  case,  for  instance,  the  same  number  of  wires  arranged 
in  groups  of  10  will  give  250  volts  at  200  amperes,  and 
arranged  5  in  parallel  will  furnish  500  volts  at  100  amperes. 
3.  Diameter  of  Armature  Core  and  Dimensions  of  Slots,  — 

By  (30),  P.  58: 

d\  —  230  x  —  =  36.8  inches. 
200 

From  Table  XV.,  p.  70,  the  approximate  size  of  the  slot  is 
if"  X  -fa*.  The  width  of  this  slot  will  accommodate  4  No. 
14  B.  W.  G.  wires,  thus: 

£s  =  (.083  +  .016")  x  4  +  2  X  .020"=  .436,   or  -j^  inch, 
the  slot  insulation,  e  —  .020",  being  taken  from  Table  XIX., 
p.  82. 

Each  conductor  being  made  up  of  20  wires,  the  number 
of  layers  in  each  slot  must,  therefore,  be  a  multiple  of  5. 
The  nearest  number  of  layers  thus  qualified  is  15,  hence 
the  actual  depth  of  the  slots,  if  .010"  is  allowed  for  separating 
the  conductors,  and  .035"  for  binding: 

h&    —  (.083"  +  .016")  x  15  +  .020"  +  2  x  .010"  4-  .035' 
=  1.6",  or  \-fy  inch. 


External  diameter  of  armature  : 

d\  =  36.8  +  i-ft-  =  385  inches. 

Diameter  at  bottom  of  slots  : 

</a    =  3&J-  -  2  x  i^V  —  35|  inches. 

Number  of  slots,  by  (34),  p.  70: 


4.   Length  of  Armature  Core.  — 
B7  (40),  P-  76: 

12   x  20  X  346        ,_  .     , 

'•  =  =  10  lnches' 


554 


DYNAMO-ELECTRIC  MACHINES. 


[§137 


5.  Arrangement  of  Armature  Winding. — The  number  of  com- 
mutator divisions  must  be  between  40  and  60,  and  must  be  a 
divisor  of  the  number  of  slots,  138,  taking  3  slots  per  com- 
mutator section,  we  have 


therefore,  by  (46),  p.  89: 

n    =  I3S  X  4  X  I5  =  9 

46    X    20 

The  armature  winding,  consequently,  consists  in  46  coils  of 
9  turns  of  20  No.  14  B.  W.  G.  wires,   each  coil  occupying  3 


Fig.  351.  —  Arrangement  of  Armature  Winding,  $o-KW  Double-Magnet 
Type,  Low-Speed  Generator. 

slots.     One  slot,  containing  3  turns,  or  one-third  of  an  arma- 
ture coil,  is  shown  in  Fig.  351. 

6.   Radial  Depth,  Minimum  and  Maximum  Cross-  Section,   and 
Average  Magnetic  Density  of  Armature  Core.  — 

By  (i38),  P-  202: 

10'       webers- 


By  (48),  p.  92,  and  Table  XXII.  : 

fc«:.4       Q9>63°'000          -=6*  inches. 
2  X  80,000  X  10  X  .9 

Internal  diameter  of  armature  core,  Fig.  352: 
35|  -  2  x  6{  =  211  inches. 


§137]       EXAMPLES  OF  GENERATOR   CALCULATION. 

Mean  diameter  of  core: 

d'\  =  21$  +  6|-f  i^-  =  30ft-  inches. 
Maximum  depth  of  core,  from  (234),  p.  342: 


555 


'•=  63A  X  /I  -  i  =  14.8  inches. 


Fig-  352. — Dimensions  of  Armature  Core,  so-KW  Double-Magnet  Type, 
Low-Speed  Generator. 

By  (232),  p.  341: 

S&1  =  2  x  10  X  6|  x  .90  =  121  square  inches. 
By  (233),  p.  341: 

S^    =  2  x  10  x  14-8  X  .90  =  266  square  inches. 

0,630,000 
ai  =          i2i~  :  ~  79,6o°  lmes  Per  square  inch. 

0,630,000 
aa  ~          266         ~  36'200  lmes  Per  square  inch. 

By  (231),  p.  341: 

/(<&'.)  =j[/ (7956oo)  +  7(36,200)]  =  3°'7  +  6-7 

=  18.7  ampere-turns  per  inch. 
Corresponding  average  density: 

&"a  =  69,000  lines  per  square  inch. 


556  DYNAMO-ELECTRIC  MACHINES.  [§137 

7.   Weight  and  Resistance  of  Armature  Winding.  — 
By  (53)  P-  99  : 


BY  (58),  P-  101: 

0/4  =  .00000303  x  137,980  x  1360  =  568  Ibs.,  bare  wire. 

By  (59),  P-  I02: 

o//'a  =  i.  066  x  568  =  605  Ibs.,  covered  wire.       > 

By  (61),  p.  105: 

r&  =  -  -  -  X  1360  X  .0015  =  .0256  ohm,  at  15.5°  C. 
4  X  20 

8.   Energy  Losses  in  Armature,  and  Temperature  Increase.  — 
By  (68),  p.  109: 

P&  =  1.2  X  4Q02  X  .0256  =  4950  watts. 
From  Fig.  352  : 


X  *  X  &&  -  138  X  iA  X-          X  10  X  .90 


1728 
=  3.61  cubic  feet; 

~  ~~  =  3>33  cycles  Per  second; 


from  Table  XXIX.  (&"a  =  69,000): 
r/  =  27.61  watts  per  cubic  foot; 

from  Table  XXXI.  (tf,  =  .020"): 
s  =  .138  watts  per  cubic  foot. 

By  (73).  P-  II2: 

jPh  =  27.61  X  3-33  X  3-61  =  320  watts; 
By  (76),  P.  120: 

Pe  =  .138  X  3.33*  X  3-61  =  6  watts. 

By  (65),  p.  107: 

A  =  4950  +  320  +  6  =  5276  watts. 


§137]      EXAMPLES  OF  GENERATOR   CALCULATION.          557 

By  (79),  P-   I25' 

5A  =  2  X  30fV  X  n  X  (10  +  6|  +  4  X   i^-) 

=  4360  square  inches. 
Ratio  of  pole-area  to  radiating  surface: 

38j  X  TT  X   10  X  .70  _ 

4360 
From  Table  XXXVI.,  p.  127,  by  interpolation: 

fi  a  -  44°  C. 
By  (81),  p.  127: 


Armature  resistance,  hot: 

r'&  =  .0256  X  (i  +  -004  X  53i°)  =  -0314  ohm,  at  69°  C. 

9.    Circumferential  Current  Density,  Safe  Capacity  and  Running 
Value  of  Armature;  Relative  Efficiency  of  Magnetic  Field.  — 
By  (84),  p.  131: 

ic  =          j  —      -  =  685  amperes  per  inch  circumference. 

Table  XXXVII.,  p.   132:  6a  =  40  to  60°  C. 
By  (88),  p.  134: 

P'  =  1.33  X  38|-2  X   10  X  .85  X  200  X  20,000  X   io~* 
=  67,000  watts. 

By  (90),  P-  135  : 

pl&  =      133  X  400     =  <0047  watt  per  pound   of  coppert 
568  X  20,ooc       at  u  ^  fidd  dengity 

By  (i55)>  P-  2II: 

0    =    9,  630,  ooo    x  5800  Webers  per  watt,  at  unit 


X 


b.    DIMENSIONING    OF    MAGNET    FRAME. 

i.   Total  Magnetic  Flux,  and  Sectional  Areas  of  Frame.— 
By  (156),  p.  214,  and  Table  LXVIII.  : 

$'  -  1.25  X  9,630,000  =  12,000,000  webers. 


558  DYNAMO-ELECTRIC  MACHINES.  [§137 

By  (217),  P.  314: 

=    12,000,000  =  ^  3         are 
90,000 

By  (220),  p.  314: 

12,000,000  =  re  i 

45,000 

2.  Magnet    Cores.  —  The    two    cores   being   magnetically    in 
parallel,  each  must  have  one-half  the  area  -5"'w.i.  found  above 
for  wrought  iron,  and  making  their  breadth  equal  to  that  of 
the  armature  core,  their  thickness  is  found: 

_33i3_  _  ^  ^  or  sav  flj  inches. 

3.  Polepieces.  —  Thickness  at  ends  joining  cores: 

2  x  6f  =  13J  inches. 
Bore,  by  Table  LXL,  p.  116: 

4,  =  38£  +  2  X  \  =  38|  inches. 
Length  of  centre  portion  (equal  to  diameter  of  armature  core)  : 

38}  inches. 

Depth  of  magnet  winding  (Table  XXX.,  p.  115): 
hm  —  2f  inches. 

Allowing  £  inch  clearance  between  the  magnet  winding  and 
the  pole-tips,  the  total  length  of  the  polepieces  is: 

38^  +  2  X  (2|  +  |)  =  45  inches. 
Pole-distance  : 

/'p  =  383-  X  sin  27°  .=  15  inches, 

which  is  4.45  times  the  total  length  of  the  gap  space  (compare 
Table  LX.,  p.  208). 

Thickness  in  centre,  required  for  mechanical  strength  only: 

3^  inches. 
Thickness  of  pole-tips: 


-  15')  =  1|  inch. 


§137]      EXAMPLES  OF  GENERATOR   CALCULATION.          559 


All  other  dimensions  of  the  frame  can  be   directly  derived 
from  Fig.  353. 


»  i 

Fig.    353. — Dimensions    of    Field-Magnet   Frame,    50   KW   Double-Magnet 
Type,  Low-Speed  Generator. 

C.    CALCULATION    OF    MAGNETIC    LEAKAGE. 

i.   Permeance  of  Gap  Spaces. — 

-  -4375  =  -439  inch; 


Ratio  of  radial  clearance  to  pitch: 

.125 

.1765 =  I43; 

Product  of  field  density  and  conductor  velocity: 

20,000  x  32  =  640,000, 
hence  by  Table  LXVIL,  p.  230,  the  factor  of  field  deflection 

*„  =  35 
and  by  (174),  p.  230: 


3.  = 


*  [3^1  X  7t  X  .70  +  (-439  +  -219)  X  138  X  .85]  Xio 
_  4  


3  X 


=        .  =  544. 

•75 


560  DYNAMO-ELECTRIC  MACHINES.  [§  137 

2.  Permeance  of  Stray  Paths.  — 
By  (194),  p.  242: 

j  (5H  +  10)  X  13*  +  3i  X  10        io  X  ij  ) 
^  =  2  j  -  18  h  15  +  i*  j 

-2(53.1  +  .9)  =  108. 

3.  Probable  Leakage  Factor.  — 

By  (157),  p.  218: 

544  -4-  108 

X   —   D^*  ~  -    =    1.20. 

544 
Ratio  of  width  of  slot  to  pitch: 

•4375  _ 
~ 


therefore,  by  (158),  p.  218,  and  Table  LXV.  : 
A'  =  1.03  X  1.20  =  1.24. 

d.    CALCULATION    OF    MAGNETIZING    FORCES. 

i.    Shunt  Magnetizing  Force. 

=  6  X  125  X_io:  =  9  Q6Q  ooo  Webers. 

414    X    200 

Air  gaps: 
<*..  =  -3133  X  9-^-°  X  .75  =  .3^33  X  22)2oo  X  .75 

=  5216  ampere-turns. 
Armature  core: 


il  x  39  =  605  ampere-turns. 


/"a  =  28|  X  n  X  ~°  "^o27°  +  6-|  +  3i  =  39  inches. 
Wrought  iron: 

38  =  36.5X38 


=  1387  ampere  turns. 


§137]      EXAMPLES  OF  GENERATOR   CALCULATION.  561 

Cast  iron: 

i.24  X  9> 


X22 


2Xl3iXlo 

.24X9r°6o,ooo\         ,./  _  9.060,000 

" 


if    /i.24X9r°o,ooo\         ,./  _  9.00,000  _  v  -• 

2     /(     2  V  T,i   y   10     J  +  '    /    ?"  ~  \ 

^(38|7rX.7)Xio  +  2Xif)-J 

" 


=  79  X  6-i  +  79+225'4  X  22  =  514  +  H48 
=  1662  ampere-turns, 

the  length  of  the  uniform  cross-section  being 
2  x  3^  =  6J  inches, 

and  the  mean  length  of  the  varying  cross-section,  by  (243), 
p.  348: 

— -  -4-  i4  4-  i4  =  22  inches. 
2 

AT&.  =  5216  -|-  605  -f-  1387  -f-  1662  =  8870  ampere-turns. 
2.   Series  Magnetizing  Force. — 

E'  =  125  -f  1.25  x  4°°  X  .0256  =  137  volts. 

*  =  6  X  I37  X  I0'  =  9,930,000  webers. 

414    X    200 

Air  gaps: 

0,030,000 
<***  =  -3!33  X  -      -a —  X  75  =  -3133  X  24,300  X  .75 


=  5710  ampere-turns. 
Armature  core: 


=  3J>_  L_Z  x  ^Q  —  820  ampere-turns. 


1  r  /  ^12,300,000^  _     f  /9,93Q, 
h2  L7  V       270       J^J  \    428. 


562  DYNAMO-ELECTRIC  MACHINES.  [§137 

Wrought  iron: 

^...=/(i-24XI93f°'ooo)x  38  =  54.2x38  : 

=  2060  ampere-turns. 
Cast  iron: 


,000  .    _ 

X    22 


=  98.6  X  6£  +  98.6  +  28.2  X  22  =  640  +  1400 

=  2040  ampere-turns. 
The  average  specific  magnetizing  force  of  the  variable  section, 

-i(98.6  +  28.2)  =  63.4, 

corresponds  to  an  average  density  of  (B"p  =  41,000  lines  per 
square  inch,  from  which  Table  XCL,  p.  352,  gives  £J4  =  1.71. 
The  maximum  density  in  the   armature   teeth,   at  normal 
load,  is: 

_  9,93°>000  __ 

7  X  -7   X  (35f  X  n  -  138  X  A)  X  10  X  .90 

0,030,000 
=  -  -  =  62,000  lines  per  square  men, 

and  for  this,  Table  XC.,  p.  350,  gives  £13  =  .36.     Hence  by 
(250),  P-  352: 

atr  =  r.7i  X  4I4  X  2°°  X    '36  RX  27°  =  3830  amp.  -turns. 

2  IOO 

.  •.  AT  =  5710  -|-  820  -f-  2060  -f-  2040  +  3830 

=  14,460  ampere-turns. 
ATse  =  14,460  —  8870  =  5590  ampere-turns. 

e.    CALCULATION    OF    MAGNET    WINDING. 

Temperature-increase  permitted,  0m  =  19°  C.      Percentage 
of  extra-resistance  in  circuit  at  normal  load,  rx  =  35  %. 


§137]      EXAMPLES  OF  GENERATOR   CALCULATION.  563 

i.  Series  Winding.  —  Apportioning  one-third  of  the  total 
winding  depth,  hm  =  2f",  to  the  series  winding  (ATse  being 
about  one-third  of  AT),  about  i  inch  will  be  taken  up  by  the 
latter,  hence,  if  the  series  coil  is  wound  next  to  the  core,  the 
mean  length  of  a  series  turn  : 

/'T  —  2  (10  -|-  6J)  -j-  i  x  n  =  36.64  inches, 
and  the  mean  length  of  a  shunt  turn: 

l\  —  2  (12  -f  8j)  -f-  if  X  7t  =  47  inches. 
The  radiating  surface  of  each  magnet  is: 
SM  =  2  (10  -j-  6f  -|-  2}  it)  x  (18"  —  i")  =  860  square  inches. 
By  (343),  P.  4oo,  thus: 


=  910,000  circular  mils. 

For  22  No.  4  B.  &  S.  wires  (.204"  -f-  .012")  the  actual  area  is: 
22  x  4J,743  =  918,346  circular  mils. 

Number  of  turns  required  per  magnetic  circuit,  if  both  coils 
are  in  series: 


By  (344),  p.  400,  for  the  two  series  coils: 

64  =  -00098 


r'8e  =  1.078  X  .00098  =  .00106  ohm,  at  34.5°  C. 
and  the  total  weight: 

7#/se  =  2  x  14  X  ~~  X  22  x  .1264  =  238  Ibs.,  bare  wire; 


w/'ge  =  1.029  X  238  —  245  Ibs.,  covered,   or  122}  Ibs.    per 
magnet. 

2.   Shunt  Winding.  —  The  two  shunt  coils  to  be  connected  in 
parallel. 
By  (318),  P.  385: 

*sh  =  -         X        X  1.35  X  (i  +  .004  x  19)  =  397  ft.  per  ohm. 


564  DYNAMO-ELECTRIC  MACHINES.  [§137 

The   nearest  gauge  wire  is  No.  14  B.  and  S.  (.064"  -j-  .007") 
with  a  specific  length  of  398  feet  per  ohm. 
By  (346),  p.  400: 


P8h  =       .  x  86o  _  400*  x  i  =  2l8  _  85  =  I33  watts. 

By  (312),  p.  383: 

^'Sh  =  133  X  1-35  =  l8°  watts. 
By  (314),  p.  384: 

^8h  =  887°  *  I25  -  6170  turns  per  magnet. 

IoO 

By  (315),  p-  384: 
Z8h  =  6170  x  ~==  24,200  feet  per  core. 

Total  weight  : 

wtsh  =  2  x  24,200  x  .01243  '=  604  Ibs.,  bare  wire. 

wt'sh—  1.0325  X  604  =  624  Ibs.,   covered,   or  312  Ibs.    per 

magnet. 

Shunt  resistance  per  core: 

=  60.8  ohms,  at  15.5°  C. 


r'8h  —  60.8  X  1.076  =  65.5  ohms,  at  34.5°  C. 
^"sh  =  65.5  x  1.35  =  88.4  ohms,  each  shunt  circuit. 
Exciting  current: 

/Bh  =  —    —  =±  1.4:2  amperes,  at  normal  load. 

00.4 

3.   Arrangement  of  Magnet  Winding  on  Cores.  — 
Number  of  series  wires  per  layer: 

— 


Number  of  layers  of  series  wire: 

JX  22 


78 
Height  of  series  winding: 

4  X  .216  =  .864  inch. 


§137]      EXAMPLES  OF  GENERATOR   CALCULATION.          565 
Number  of  shunt  wires  per  layer: 

17    =210. 


.071 
Number  of  layers  of  shunt  wire: 

6l70   _    og 

Height  of  shunt  winding: 

26  x  .071  =  1.84:6  inch. 

Allowing  .1   inch   for  core  covering  and   insulation  between 
layers,  the  actual  total  depth  of  magnet  winding  is: 

hm  —  .864  +  1.846  -j-  .1  =  2{$  inches. 
Actual-magnetizing  force  at  full  load: 


AMPERE- 
TURNS. 


Series  magnetizing  force,  ATae=  14  x  4°°  =        5600 

Shunt  magnetizing  force,  ATsh=  26  X  240  X  1.42  =        8850 


Total  magnetizing  force,    .         .         .         .   A  T  =14,4:50 

/.    CALCULATION    OF    EFFICIENCIES. 

i.  Electrical  Efficiency.  —  By  (353),  p.  406: 

-,    —  __  _  125  X  400 

Ye  —  ~  -  jjg- 

125  X  400  +  (400  +  2  X  i.42>2  X  .0314  +  400*  X  .00106  -f  (2  X  i-42)a  X  — 


2.    Commercial  Efficiency.  —  Allowing  2500  watts  for  commuta- 
tor- and  friction-losses,  we  have  by  (361),  p.  408: 


= 


55,630  +  332  +  2500       58,462 

3.    Weight  Efficiency. — The  estimated  weights  of  the  different 
parts  of  our  dynamo  are: 

Armature: 

Core,  3.56  cubic  feet  of  wrought  iron,  ,  .'  1710  Ibs. 

Winding,  insulation,  binding,  etc.,     .  ;  ,,  640     " 

Shaft,  commutator,  spiders,  etc.,       .  .  500    " 

Armature    complete,  .         .         ;.        .        2850  Ibs. 


566  DYNAMO-ELECTRIC  MACHINES  [§138 

Frame  : 

Magnet  cores,    2  x  45  X  10  X  6f-  =  6075 

cubic  inches  of  wrought  iron,         .     -  ;       1700  Ibs. 
Polepieces, 

[45  X  45  ~  (38f  X  |  +  2  X  18  X  3i  + 

2  x  15  X  if)]  X  10  =  6970  cubic  inches  of 

cast  iron,  .  .  .  .  .  1800  " 

Field  winding  and  insulation  (250  -{-  650) 

Ibs  =  .  .  .  .  .-  .  .  900  " 

Dynamo  portion  of  bed,  bearings,  etc.,     .          750 


" 


Frame,  complete,        .         .         .  .  .         5150  Ibs. 
Fittings: 

Brushes,  holders,  and  brush-rocker,    .  ".. .,  loo.lbs. 

Switches,  series  field  regulator,  cables,  etc.,  100    " 

Fittings,  complete,      .      .  ,..         .         .  •      ;  200  Ibs. 


Total  net  weight  of  dynamo,     -.         .         .        8200  Ibs. 
The  specific  output,  therefore,  is: 

-  r-  6.1  watts  per  pound. 

138.  Calculation   of  a   Multipolar,    Multiple  Magnet, 
Smooth  Ring,  High-Speed  Shunt  Dynamo  : 

1200  Kilowatts.    Radial  Innerpole  Type.    10  Poles. 

Cast  Steel  Frame. 
150  Yolts.   8000  Amps.    232  Revs,  per  min. 

a.    CALCULATION    OF    ARMATURE. 

i.   Length  of  Armature  Conductor.  —  Taking 


Table  IV.,  p.  50,  gives: 

e  —  60  x  io~8  volt  per  foot; 
Table  V.,  p.  52: 

vc  =  96  feet  per  second; 


§138]      EXAMPLES  OF  GENERATOR   CALCULATION.          567 

and  Table  VIII.,  p.  56: 

E'  =  1.02  x  150  =  153  volts. 

This  machine  being  of  comparatively  low  voltage  and  high 
current  strength,  the  field-density  obtained  from  Table  VI.  is 
reduced  according  to  the  rule  given  on  page  54,  thus: 

3C"  =  f  X  60,000  =  40,000  lines  per  square  inch. 
Consequently,  by  (26),  p.  55: 

=     5  X  153  X  io-    =  332  feet 

60  X  96  X  40,000 

2.  Area  and  Shape  of  Armature  Conductor. — By  §  20: 


tfa2  =  600  X  ^-  =  961,000  circular  mils. 

In  this  case  we  will  employ  a  wedge-shaped  conductor,  the 
external  surface  of  the  armature  being  used  as  a  commutator. 
The  height  of  the  winding  space,  by  Table  XVIII.,  p.  75,  is 
h&  =  .75  inch,  from  which  is  to  be  deducted  .100  inch  for  core 
insulation  (column  a,  Table  XIX.,  p.  82),  and  .025  inch  for 
thickness  of  bar  covering  (half  of  the  .050  inch  insulation  be- 
tween two  bars,  column  e,  Table  XIX.),  leaving  .625  inch  for 
the  height  of  the  armature  conductor,  whose  mean  width 
on  the  internal  periphery,  therefore,  is: 

7t 

960,000  x 

— 6-  =  1.2  inch. 
.625  X  io6 

This  making  too  massive  a  single  conductor,  we  divide  it 
into  4  bars  of  .3  inch  average  width. 

3.   Diameter  of  Armature  Core,  Number  of  Conductors. — 

By  (30),  p-  58: 

06 
<4  =  230   x  —  =  96  inches, 

being  rounded  off  to  the  next  higher  even  dimension,  since  in 
this  case  d&  is  the  internal  diameter  of  the  armature.  The 
mean  winding  diameter,  therefore: 

^a  =  96  —  2  x  .  125  —  .625  =  95-J-  inches, 


568  DYNAMO-ELECTRIC  MACHINES. 

and  the  number  of  armature  conductors: 


[§138 


95J   X 


4X  (-3+  •' 

4.  Length  of  Armature  Core. — 
By  (40),  p.  76: 

12x332   =<>Q  inches. 

200 

5.  Radial  Depth,  Minimum  and  Maximum  Cross- Section,   and 
Average  Magnetic  Density  of  Armature  Core. — 

By  (137),  P.  201: 

=  6_X5X.53Xio'  g  99  ooo,000  webers. 

200    X    232 

By  (48),  p.  92,  and  Table  XXII.: 
99,000,000 


=  8  inches. 


10  X  70,000  X  20  X-9O 
External   diameter  of  armature  core,  Fig.  354, 


Fig-  354- — Dimensions  of  Armature  Core,  I2OO-KW  ID-Pole  Radial 
Innerpole-Type  Generator. 

d\  —  96  -f  2  x  8  =  112  inches. 
Mean  diameter  of  armature  core, 

d'"&  —  96  -f-  8  =  104  inches. 
The  width  of  one-half  field  space  is 

x.  78  =  »  inches, 


§138]      EXAMPLES  OF  GENERATOR   CALCULATION.          569 
hence,  by  Fig.  354: 


b'&  =  Vi2a  -|-  82  =  14!  inches. 
By  (232),  p.  341  : 

S&1  =  10  x  20  x  8  X  .9  =  14,400  square  inches. 

B7  (233),  P-  34i: 

Sa2  =  10  x  20  x  144  X  .9  =  28,100  square  inches. 

By  (231),  P-  34i: 


l8-5  +6.5 

-   "— 


14,400  28,100 

=  12.5  ampere-turns  per  inch. 
Average  density: 

(B"a  —  58,750  lines  per  square  inch. 

7.   Size   of  Armature    Conductor;     Weight  and  Resistance   of 
Armature  Winding.  — 

From  Fig.   355  the  exact    size  of  the  armature   bars   is  ob- 
tained as  follows: 


Fig.  355. — Dimensions  of  Armature  Conductor,  I2OO-KW  lO-Pole 
Radial  Innerpole-Type  Generator. 

Minimum  thickness  of  bar  on  inner  circumference: 
94j  X  TT 


4  X   200 


-  .050"  =  .3211  inch. 


57°  DYNAMO-ELECTRIC  MACHINES,  [§138 

Maximum  thickness  of  bar  on  inner  circumference: 
_5    _  .050'  =  .3260  inch.' 


Minimum  thickness  of  bar  on  outer  circumference: 


Maximum  thickness  of  bar  on  outer  circumference: 

ii3iX  n  __  =t3957inch. 

4  X  200 

Area  of  conductor  on  inner  circumference: 

(tfa)a  =  4  x  625  x  32I'r  +  326.0  =  808^875  square  mils 
Area  of  conductor  on  outer  circumference: 

(d'ay  =  4  x  625  X  390.8  +  395.7  =  983^25  square  mils. 

Mean  length  of  armature  turn: 

2  x  (20  -f-  8  -f  2  x  |)  =  59J-  inches. 
Total  length  of  armature  winding: 


T        200  x 
Zt  =  --  2.  1  —  992  feet. 

Weight: 

(808,875  +  983,125)! 
wt&  —  .00000303  x  —  —  X  992  =  3440  Ibs. 

Armature  resistance: 

r&  =  —  l—-*  x  992  X  -  ^  -  =  .000091  ohm,  at  15.5°  C. 
896,000  x  ^ 

7T 

8.   Energy   Losses  in  Armature,  and  Temperature  Increase.  — 
By  (68),  p.  109: 

P*  =  1.2  X  8ooo2  X  .000091  =  7000  watts. 


£138]      EXAMPLES  OF  GENERATOR   CALCULATION.          571 


...        104  XTT  X  20  X  8  X  .9  u-    r 

M  =  -  y  =  27.2  cubic  feet. 

1728 

^V",  =  -£—  X  5  =  19.33  cycles  per  second. 

From  Table  XXIX.,  p.  113,  (for  &"a  =  58,750): 

rj  =  21.35. 
From  Table  XXXI.,  p.  116,  (for  ^  =  .015"): 

c  =  .0258  X  i-5a  =  .058. 
By  (73),  P-  112: 

A  =  21.35  X  19.33  X  27.2  =  11,220  watts. 
By  (76),  p.  120: 

Pe  =    .058  x  19. 332  X  27.2  =  580  watts. 

By  (65),  p.  107: 

p^  =  7ooo  -f  11,220  +  580  =  18,800  watts. 
By  (79),  P-  125: 

5A  =  2  x  104  x  n  x  (20  -f-  8  +  4  X  f)  =  20,250  sq.  ins. 
Ratio  of  pole  area  to  radiating  surface : 

94  X  it  X  20  X  .78  _ 
20,250 

From  Table  XXXVI.,  p.  127: 
By  (81),  p.  127: 


20,250 

Armature  resistance,  warm: 
r'&  =  .000091  X  (i  +  -004  X  37i°)  =  ,000105  ohm,  at  53°  C. 

9.    Circumferential  Current  Density,  Safe  Capacity  and  Running 
Value  of  Armature;  Relative  Efficiency  of  Magnetic  Field. — 

By  (84),  p.  131  = 
8000 

200    X    

*c  =  -  ~  =  490  amperes  per  inch  circumference. 

104  X  7t 


572  DYNAMO-ELECTRIC  MACHINES.  [§138 

%  (88),  p.   134: 

P'  =  96*  x  20  x  .85  x  232  x  40,000  x  io-8  =  1,510,000 
watts. 

By  (90),  p.  135: 

p,    =     153  X  8000    _  watt  copper,  at  unit 

3440  X  40,000 

density. 


=   777()  webers 


99,000,000 
153  X  oooo 

velocity. 

b.    DIMENSIONING    OF   MAGNET    FRAME. 

1.  Total  Magnetic  Flux,  and  Sectional  Area  of  Frame.  — 
By  (156),  p.  214,  and  Table  LXVIII.  : 

$'  =  1.  12  X  99,000,000  =  111,000,000  webers. 
By  (218),  p.  314: 

0  I  IT,  OOO,OOO  tn*t\  -       u 

SCB  =  -  -  —     -  =  1310  square  inches. 
85,000 

2.  Magnet  Cores.  —  There  being  io  magnetic  circuits  through 
the   io  cores,   each  circuit  containing  two  of  the  magnets  in 
series,  the  sectional  area  of  one  'core  must  be  one-fifth  of  the 
total  frame  area  obtained;  making  the  breadth  of  the  cores  19J 
inches,  that  is,  £  inch  narrower  than  armature  and  polepieces, 
their  thickness  is  found  : 


— -  =  13J  inches. 

The  length  of  the  cores  is  obtained  from  Table  LXXXIIL, 
p.  321,  the  nearest  cross-section  being  12  x  24  inches,  for  which 

/m  =  16  inches. 

3.  Polepieces. — External  diameter  of  field   frame,   by  Table 
LXI.,  p.  209: 

</p  =  96  -  2  x  (J  -f  J)  =  94  inches. 


§138]      EXAMPLES  OF  GENERATOR   CALCULATION.          573 

Distance  between  pole-corners: 

/P  =  94  X  sin  4°  =  6J  inches. 

This  is  not  as  large  as  given  by  Table  LX.,  p.  208,  but  is 
sufficient  for  the  radial  innerpole  type.  Taking  3  inches  for 
the  centre  thickness  of  the  polepieces,  their  dimensions  are 
derived  as  follows: 

Width  of  plane  face : 

2  X  (  —  —  3  \  X  tan  14°  =  22  inches. 


Width  of  curved  face: 

94  X  sin  14°  =  22f  inches. 
Thickness  of  pole  tips: 

9-  -3 

=  1     inch. 


2  COS  14° 

4.    Yoke.  —  Making  the  width  of  the  yoke 

i9t+2  X  i  =  20J  inches, 
its  radial  thickness  must  be: 

-±^_  -  6}  inches. 

10   X    20^ 

From  Fig.  356,  the  diameter  across  flats  is: 

94  —  2  x  (3  +  16)  =  50  inches. 
Diameter  across  corners: 

3&  =  59  inches- 

Length  of  side  of  decagon: 

56  X  sin  18°  =  17}  inches. 

C.    CALCULATION    OF  MAGNETIC    LEAKAGE. 

i.   Permeance  of  Gap  Spaces.  — 

OC"   X  7'c    =    40,000   X    96   =  3,840,000; 
by  Table  LXVI.,  p.  225,  £ja  =  1.40;  hence,  by  (167),  p.    226: 

7(94  +  96)  X  n  X  .85 


_ 
1.40  X  (96  -  94)  "    2.8 


574 


DYNAMO-ELECTRIC  MACHINES. 


[§138 


2.  Permeance  of  Stray  Paths.—  Distance    apart  of  cores,  at 
yoke-end: 

^  —  (171  __  13 j)  x  cos  18°  —  3.6  inches. 

Distance  apart  of  cores,  at  pole-end: 


-6  X 


—  13.6  inches. 


tan  18' 


Fig-  356.  —  Dimensions  of  Field-Magnet  Frame,  I2OO-KW  lo-Pole  Radial 
Innerpole-Type  Generator. 

Projecting  area  of  polepiece: 

Si  —  22  X  20  —  19^  X  13^  =  177  square  inches. 
Projecting  area  of  yoke: 

S^  =  20^  x  iyi  —  i9i  X  13!-  =  91  square  inches. 
Total  stray  permeance,  from  Fig.  356  : 


=  10  x  (18.1  +  4-6  4-  4.2)  =  269, 


§138]      EXAMPLES  OF  GENERATOR   CALCULATION.          575 
3.   Probable  Leakage  Factor,  and  Total  Flux. — 

By  (157),  P.  218: 

A   =  g?  +  269  =  £176  = 
907  907 

<£7  =  1.295  x  99,000,000  =  128,000,000  webers. 
This  increased  flux  will  bring  up  the  density  in  the  frame  to 

128,000,000 
=  5  X   19^  X    i3i  ==  97>500  llnes  per  square  mch> 

which,  however,  is  within  the  practical  limits  of  magnetization 
for  cast  steel  (see  Table  LXXVI.,  p.  313),  making  a  re-dimen- 
sioning of  the  frame  unnecessary. 

d.    CALCULATION    OF    MAGNETIZING    FORCES. 

1.  Air  Gaps. — Actual  density:  ^ 

99,000,000 
^"  =  — 2C4o —  =  39,000  lines  per  square  inch. 

By  (228),  p.  339: 

afg  —  '3*33  X  39,000  X  2.8  =  34,200  ampere-turns. 

2.  Armature  Core. — 
By  (236),  p.  343: 

25T+4 

l\  =  104  X  7f  x  -$-2 h  8  =  28  inches; 

360 

/(&"a)  =/(58,75o)  =  12.5  ampere-turns  per  inch. 

By  (230),  p.  340: 

at&  =  12.5  X  38  =  350  ampere-turns. 

3.  Magnet  Frame. — Length  of  path  (see  Fig.  356): 

2  X  (3i  +  1 6  +  3£  +  4J)  =  54  inches. 
For  cast  steel, 

/  (97, 500)  =  86  ampere-turns  per  inch. 
By  (238),  p.  344: 

a/m  —  86  x  54  =  4650  ampere-turns. 


576  DYNAMO-ELECTRIC  MACHINES.  [§138 

4.  Armature  Reaction.  —  Mean  density  in  polepieces: 

5   X^Tx^o  =  57.*°°  Hnes  per  square  inch.-"   " 
hence  by  (250),  p.  352,  and  Table  XCI.  : 
at,  =  ,.as  x  2°°  X  8oo°    X  -£-  =  MfiO  ampere-turns. 

IO  loO 

5.  Tk/fc/  Magnetizing  Force  Required.  — 
By  (227),  p.  339: 

A  T  —  34,  200  +  350  +  4650  -f  4450  —  43,650  ampere-turns. 

e.    CALCULATION  OF  MAGNET  WINDING. 

In  the  present  machine  the  winding  space  is  limited  by  the 
shape  of  the  frame,  the  height  available  at  the  pole  end  of  the 
core  being  4  inches,  and  at  the  yoke  end  only  1}  inch,  see  Fig. 
356.  The  larger  depth  can  be  employed  until  the  distance 
between  two  adjoining  coils  becomes  the  same  as  that  allowed 
at  the  yoke  end;  leaving  j-  inch  for  the  bobbin  flanges,  and  for 
insulation  and  clearance,  it  is  thus  found  that  8J  inches  of  the 
available  length  of  each  core  can  be  wound  4  inches  deep,  and 
that  for  the  remaining  7  inches  the  winding  depth  tapers  from 
4  inches  to  i  J  inch.  This  gives  a  mean  winding  depth  of 

4    X  8f  +  L(4  +  i|)X7 

=  3    inches. 


m 

Mean  length  of  one  turn: 

/T    =  2(19^  -|-  13!)  -f  3^  x  7t  —  77  inches. 
Radiating  surface  of  each  magnet: 

S*  =  2  (19^  -f  13^+  3i  X  ?r)  X  i5f  —  1585  square  inches. 

By  means  of  formula  (328),  p.  390,  we  can  now  determine 
the  minimum  temperature  increase  that  can  be  obtained  with 
the  present  design  (by  entirely  filling  the  given  winding  space). 
The  weight  of  bare  copper  wire  filling  one  bobbin  is,  by  (330), 
p.  390: 

o^m  =  77  X  i5f  X  3^  X  .21  =  890  pounds. 


EXAMPLES  OF  GENERATOR   CALCULATION.  577 

hence  by  (329),  p.  390: 

\  « 

75  j 


x  x  x 

"  X 


12 '        I38s"          =  44°  C 


890   --    .004    x  [31-3  X  140  2  X 


Although  this  is  rather  high,  especially  for  so  large  a 
machine,  it  is  yet  within  practical  limits,  and  we  therefore 
base  the  winding  calculation  on  the  above  dimensions  of  the 
winding  space. 

Connecting  the  10  coils  in  5  groups  of  2  each,  the  terminal 
voltage  of  150  volts  will  correspond  to  the  total  magnetizing 
force  of  one  circuit,  and  formula  (318),  p.  385,  gives  the  specific 
length  of  the  wire  required,  for  20  per  cent,  extra-resistance: 

A8h   =    4^50    x    77  x  r  2Q  x  (l  H_    OQ4  x  440)  =  2635 

150  12 

feet  per  ohm. 

No.  8   B.  VV.  G.  wire  (165"   +  .010")  has  a  specific  length 
of  2637  feet  per  ohm. 
By  312,  p.  383: 

^'8h  =  ~  -  X  2  x  1480  x  1.20  =  2080  watts  per  magnetic 

circuit. 
By  (314),  p.  384: 

^sh  =  43,650  x  150  =  3150  turns  per  d 

2OOO 


3150    X    2080 
—  ~  — 


=  20,200  feet,  per  pair  of  magnets. 
=  7.67  ohms,  2  coils  in  series,  at  15.5°  C. 


By  (318),  P.  385: 


—  7-  6  7  X  (i  +  .004  X   44)  =  9.0  ohms,  one  group, 

at  59-5°  C. 


578  DYNAMO-ELECTRIC  MACHINES.  [§138 

B7  (317)  P-  384: 

r"sb   =  9-0    X    1.20  —   10.8  ohms,   one  shunt  branch,  at 

normal  load. 

.•.     /8h    =     '5°    =  13.9  amperes,  current  in  each  branch. 
10.8 

There  being  5  magnetic  circuits  with  their  magnetizing  coils 
in  parallel,  the  total  exciting  current  is: 

J3-9  X  5  =  69.5  amperes, 

while  the  joint  shunt  resistance  of  the  10  coils  is: 
9.0 


=  1.8  ohm,  at  59.5°  C. 


Total  weight: 


w/sh  =  5X7-7  _  g£3Q  pouncis   bare  wire. 
.0046 

wt'sh  =  8330  x  i. 022 1  =  8530  pounds,  covered  wire, 
or  853  pounds  of  No.  8  B.  W.  G.  wire  per  core. 
Actual  magnetizing  force  at  full  load: 

AT  —  3150  x  13.9 .  =  43,800  ampere-turns. 

Since  in  this  example  the  dimensioning  of  the  winding  space 
was  the  starting  point  of  the  winding  calculation,  no  checking 
of  the  result  with  reference  to  the  length  of  mean  turn,  radi- 
ating surfaces,  etc.,  is  necessary. 

/.     CALCULATION    OF    EFFICIENCIES. 

1.  Electrical  Efficiency. — 

^y  (352)>  p.  406: 

_  150  X  8000 

"  150  X  8000  +  8069.5"  X  .000105  +5  X  13.9*  X  10.8 

1,200,000 

=  -     -  =  .987,  or  98.7  %. 
1,217,200 

2.  Commercial  Efficiency. — Taking  the  commutation-  and  fric- 
tion-losses at  40,000  watts,  we  obtain  by  (360),  p.  407: 

_  1,200,000  _  1,200,000 

1,217,200+  1 1, 800 +  40,000        1,269,000 

or  94.7  %. 


§138]      EXAMPLES  OF  GENERATOR   CALCULATION.          579 

3.    Weight -Efficiency. — The  weight  of  the  machine  is  obtained 
as  follows: 

Armature: 

Core,  27.2  cu.  ft.  of  wrought  iron,     13,000  Ibs. 
Winding  and  insulation,  etc.,        .       4,000    " 
Armature  spider,  shaft,  etc.,        .       8,000    " 


Armature,  complete,  ....     25,000  Ibs. 

Frame : 

Magnet  cores,  10    x  19^    X    13^ 
X  16  =  42,100  cu.  ins.   of  cast 
steel,  -    .         .     1 1, 500  Ibs. 

Polepieces,  10  X  22|  X  20  X   2J- 

—  10,050  cu.  ins.  of  cast  steel,         2,800    " 

Yoke,  L  735  x  592  -  43*  j  )  X  20*- 

=  20,500  cu.  ins.  of  cast  steel,        5,700    " 

Field  winding,  spools,  and  insula- 
tion), ...  10,000  " 

Flange  for  fastening  yoke  to  en- 
gine frame,  outboard  bearing, 
etc.,  .  .  .  .  .  12,000  " 


Frame,    complete,  '".         .     42,OOo  Ibs. 
Fittings: 

Brush  shifting  and  raising  de- 
vices, brushes,  studs,  etc.,  1       3,000  Ibs. 
Switches,  cables,  etc.,           .  .       1,000    " 

•    Fittings,  complete,       .  .         .         .         .       4,000  lbs. 


Total  net  weight  of  dynamo,        .  71,000  Ibs. 

Weight  efficiency: 

1,200,000 


71,000 


—  16.9  watts  per  Ib. 


5^0  DYNAMO-ELECTRIC  MACHINES.  [§139 

139.  Calculation  of  a  Multipolar,  Single  Magnet,  Smooth 
Ring,  Moderate  Speed  Series  Dynamo  : 
30  KW.    Single   Magnet    Innerpole    Type. 
6  Poles.     Wrought-Iron  Core.    Cast  Steel  Polepieces. 
600  Yolts.     50  Amps.     400  Revs,  per  Min. 

a.    CALCULATION    OF    ARMATURE. 

1.  Length  of  Armature  Conductor.  — 

A  -  .75;  «  =    '8°   (V  '75)  =  7iV  =  57-5  X  ID-'  v.  p.  ft. 

#c  =  60  feet  per  second;  JC"  =    15,000  lines  per  square  inch; 
E'  =  1.10  X  600  =  660  volts. 

By  (26),  p.  55: 

Za  =     3x660x10-     = 

57.5  X  60  X  15,000 

2.  Sectional  Area  of  Armature  Conductor.  — 
BY  (27).  P-  57: 

<V  =  300  X  ^  =  5000  circular  mils. 

O 

No.  15  B.  W.  G.  (.072"  -f-  .016")  has  a  cross-section  of  5184 
circular  mils. 

3.  Diameter  of  Armature  Core,  and  Number  of  Conductors.  — 

By  (30),  P-  58: 

d&  =  230  X  —  =  35  inches. 
400 

The  diameter  over  the  winding  on  the  internal  circumfer- 
ence being  about  34  inches,  and  3  layers  with  its  insula- 
tions making  a  well-proportioned  winding  space  for  the  case  in 
question,  the  total  number  of  conductors  on  the  armature  is: 


= 


.072    -f-    .Ol6 

Actual  depth  of  winding: 

h&  =  3  X  (.072"  +  .016")  -f  .060"  —  .324  inch. 


£139]      EXAMPLES  OF  GENERATOR   CALCULATION.          5Sl 

4.   Length  of  Armature  Core.  — 
By  (48),  p.  92: 


4  =      _   =  13  inches. 
3600 

5.  Arrangement  of  Armature  Winding.  — 

By  (45),  p-  89: 

.     x  660  X  3 

K)min  =          II<5         =    172. 

Taking  180  commutator  divisions,  we  have  30  coils  of  20 
convolutions  per  pole. 

6.  Radial  Depth,  Minimum  and  Maximum  Cross-  Section,  and 
Average  Magnetic  Density  of  Armature  Core.  — 

Ky  (138),  P.  202: 


3600  X  400 
By  (48),  p.  92  : 

8,250,000 


= 


=  24  inches. 


6  X  50,000  X  13  X  .85 
External  diameter  of  armature- core: 

35  +  2  X  2j-  =  40  inches. 
Mean  diameter  of  armature  core: 

d'"A  =  35  +  2|  =  37^  inches. 
Maximum  depth: 

b'    = 


92  -j-  2j2  =  7f  inches. 

Deducting  f  inch  taken  up  by  armature  bolt  and  insulation, 
the  minimum  core  depth  is  reduced  to  2 J  —  j-  =  i  J  inch ;  .hence 

5ai  =  6  x  13  X  if  X  .85  =  116  square  inches. 
5aa  —  6  x  13  X  7|  X  .85  =  514  square  inches. 


582  DYNAMO-ELECTRIC  MACHINES.  [§139 

and  by  (231),  p.  341: 

/ymM  --   T/Y8>25°>000^  I    f(%>25°>°°°\1  _  20-5  +  2-9 
-  l|/V~6  ~/+/V     5«4     yJ"      ~ 

=  11,7  ampere-turns  per  inch. 

Average  density: 

&"a  =  57,000  lines  per  square  inch. 
7.    Weight  and  Resistance  of  Armature  Winding.  — 

By  (53),  p.  99: 


zt  =  .     .  x  38?o  =  95oo  feet 

By  (58),  p.  101: 

wt&  —  .00000303  x  5184  X  9500  =  149  Ibs. 

By  (59),  P-  I02: 

wt\  —  1.078  x  149  ~  161  Ibs. 
By  (61),  p.  105: 

ra  =        *     a  X  9500  =  .002  =  ,528  ohm,  at  15.5°  C. 
4X3 

8.   Energy  Losses  in  Armature,  and  Temperature  Increase.  — 
M  =  37i  X  n  X  .3  Xjj.  X  :,8j  =  f  g 

1728 


^  —          x      _  2Q  CyCies  per  second. 
60 

By  (68),  p.  109: 

A  =  1.2  X     so2  X  .528  =  1585  watts. 

By  (73),  p.  112: 

A  =   20.35  X  20  X  1.89  =  780  watts. 
By  (76),  p.  120: 

P*  =  .094  X  2o2  X  1.89  —   70  watts. 
By  (65),  p.  107: 

/>A  =  1585  +  780  +  70  =  2435  watts. 

By  (79),  P-  I25- 

SA  =  2  X  37i  TT  X  (13  +  24-  +  4  X  |)  =  4000  sq.  ins. 


$139]      EXAMPLES  OF  GENERATOR   CALCULATION.  583 

Ratio  of  pole  area  to  radiating  surface  : 

34  x  n  X  13  X  -75  =    26 

4000 
By  (81),  p.  127: 


ea  =  42  x         -  25i°  C. 

4000 

r'&  =  (i  +  .004  X  25^)  X  .528  =  .583  ohm,  at  41°  C. 

b.    DIMENSIONING    OF    MAGNET    FRAME. 

1.  Total  Magnetic  Flux,  and  Sectional  Areas  of  Frame.  — 
By  (J56),  P-  2I4- 

#'  =  1.30  x  8,250,000  =  10,700,000  webers. 

By  (217),  P.  3M: 

=  10,700,000  =  119          re  inches 
90,000 

By  (218),  p.  314: 

10,700,000 

,SC8  =  -  -  =  126  square  inches. 

85,000 

2.  Magnet  Core.  —  The    magnet   being  hollow,    its     internal 
diameter  must  be  determined  first. 

Diameter  of  shaft,  by  (123),  p.  185: 


=  i-3  X  /i/3—  —  -  =  4  inches. 
400 


Making  the  hole  in  the  core  4^  inches  in  diameter,   the  ex- 
ternal core  diameter  becomes: 


dm  =  \/  ("9  +  J5-9)  X  ~  =  13  inches. 

3.   Polepieces.  — 

^P  =  35  -  2  X  (.324  +  |)  =  34  inches, 
/'p  =  34  x  sin  7j°  =  4|  inches. 

Providing  the  same  distance  between  all  projecting  portions 
of  opposite  polarity,  the  shape  shown  in  Fig.  357  is  obtained, 
having  a  mean  width  of  about  12  inches  per  magnetic  circuit. 
The  axial  thickness  of  the  polepieces,  therefore,  must  be: 


584  DYNAMO-ELECTRIC  MACHINES. 

126  rt.   .      , 

—  31  inches, 

3X12 

leaving  the  length  of  the  magnet  core: 

4,  =  '3  -  2  X  3i  =  6  inches. 


[§139 


Fig.  357. — Dimensions  of  Armature  Core  and  Field  Magnet  Frame,   3O-KW 
6-Pole,  Single-Magnet  Innerpole  Type,  Moderate-Speed  Generator. 

C.    CALCULATION    OF    MAGNETIC    LEAKAGE. 

i.   Permeance  of  Gap  Spaces. — 

OC"  X  #c  =  15,000  X  60  =  900,000. 

By  (167),  p.  226: 

+  35)  X  n  x  .835  X  13 


_4 


1-25  X  (35  ~  34) 
2.   Permeance  of  Stray  Paths.  — 
From  Fig.  357: 


=  ^  =  520. 


6X  (2  X  I3+I2X3J) 


=  53-3  +  90-7  =  144. 


§139]      EXAMPLES  OF  GENERATOR   CALCULATION.          585 
3.   Probable  Leakage  Factor. — 

S3o+.44  =  1J88 

520 

d.    CALCULATION    OF    MAGNETIZING    FORCES. 

1.  Air  Gaps. — Actual  density: 

OC"  —    >25°>000  _  I4)000  lines  per  square  inch. 
59° 

By  (228),  p.  339: 

afg  —  -3X33  X  M»ooo  X  1.25  =  5480  ampere-turns. 

2.  Armature  Core. — 
By  (236),  p.  343: 

?+7** 

l\  =  37^  X  4— £ h  H  =  *4t  inches; 

From  Table  LXXXVIII.,  p.  336,  for  wrought  iron: 

/ (57,000)  =11.7  ampere-turns  per  inch; 
By  (230),  p.  340: 

at&  =  11.7  X  i4f  =  170  ampere-turns. 

3.  Magnet  Frame. — Wrought  iron  portion: 

Length,  /"w.i.  =  6  +  3i  +  i  —  10  inches. 

Area,      »Swi.    —  (13*  —  4^a)  -  =  116.8  square  inches. 

4 

Specific  magnetizing  force, 

/  ((Bw.i.)  =/ (92,000)  =  56.5  ampere-turns  per  inch. 
Magnetizing  force  required, 

#/wi  =  56.5  x  10  =  565  ampere-turns. 
Cast  steel  portion:     Length, 

^c.s.  =  2  X  (9i  +  6)  =  304  inches. 
Minimum  cross-section, 

•Sc.8.,  =3Xio-J-X3-J-=no  square  inches. 


586  DYNAMO-ELECTRIC  MACHINES.  [§139 

Maximum  cross-section, 

^c.s.  a  =  3  X  18  X  34  =  189  square  inches. 
Average  specific  magnetizing  force, 

10,700,000 


=  —       — -  •=.  50.5  ampere-turns  per  inch. 

Magnetizing  force  required: 

0/C8   =  50.5  x  3°i  =  1540  ampere-turns. 

4.  Armature  Reaction. — Density  in  polepieces: 

_,,  10,700,000  ..  , 

(B  p  =  -  -  =  20,500  lines  per  square  inch. 

jX  34  X  *  X  .75  X  13 

By  (250),  p.  352: 

att  =  1.25  X  3<3°0  x  *°  x  1|!  =  3130  ampere-turns. 

5 .  Total  Magnetizing  Force  Required.  — 
By  (227),  p.  339: 

AT=  5480+170  +  565  +  15^0+3130  =  10,885  ampere-turns. 

e.    CALCULATION    OF    MAGNET    WINDING. 

Limit  of  temperature  increase,  em  =  22°  C. 
By  (287),  p.  374: 

N~  =  — — -  —  218  turns. 


Allowing  a  winding  depth  of  7  inches,   the  mean  length  of 
one  turn  is 

^  =  (13  +  7)  X  n  —  62.8  inches; 

hence,  by  (288),  p.  374: 

218  X  62.8 
Ae  = =  1140  feet. 

8^  =  27  X  7t  X  6  +  6  X  14  X  3  =  760  square  inches. 

r^  :=  ~x  ^  X  — : =  .082  ohm,  at  15.5°  C. 

75        5o         i  +.004  X  22 

Ase  -  IT^-  =  13,900  feet  per  ohm. 
.002 


§140]      EXAMPLES  OF  GENERATOR   CALCULATION.          587 

The  coil  being  round  and  of  comparatively  large  diameter, 
a  single  wire,  No.  00  B.  W.  G.  (.380"  +  .020")  can  be  em~ 
ployed  without  difficulty. 

Number  of  turns  per  layer: 

5i  n 

.38  +   .02 

Number  of  layers: 


Net  depth  of  winding  space : 

h'm  —  17  X  (.38  -f  .02)  =  6.8  inches. 

Adding  to  this  the  thickness  of   the  bobbin  and   insulation, 
we  have  ^m  —  7  inches,  as  above. 
Weight  of  winding: 

wtse  =  1140  X  .437  —  500  Ibs.,  bare  wire: 
wt'se  =  1.022  x  500  =  510  Ibs.,  covered  wire. 

Resistance: 

rK  =  500  X  .00016  =  .08  ohm,  at  15.5°  C. 

Actual  magnetizing  force: 

ATae=  13  X  17  X  50  =  11,050  ampere-turns. 

14:0.  Calculation  of  a   Multipolar,    Multiple    Magnet , 

Toothed-Ring,  Low-Speed  Compound  Dynamo : 
2000  KW.    Radial  Outerpole  Type.    16  Poles.    Cast- 
Steel  Frame.     Drum-Wound  Ring  Armature. 
540  Yolts.    3700  Amps.    70  Revs,  per  Min. 

a.    CALCULATION    OF    ARMATURE. 

i.   Length  of  Armature  Conductor. — 
For  /3l  =  .  70,  we  have 

180(1  —  .70) 

16 
and 

ft  =  3^r  -  2  x  31  =  '51°. 


588  DYNAMO-ELECTRIC  MACHINES.  [§  14O 

From  Table  IV.,  p.  50: 

e  =  55  X  io~8  volt  per  foot; 

~  =  ^j-  X  io~8  =  6.875  X  io~8  volt  per  foot. 
nv       8 

From  Table  V.,  p.  52: 

vc  —  42.8  feet  per  second. 
From  Table  VI.,  p.  54: 

OC"  =  35,000  lines  per  square  inch. 
From  Table  VIII.  ,  p.  56: 

E'  —  1.02  X  540  —  551  volts. 

By  (26),  p.  55: 

8  feet 


a 

6.875  X  42-8  X  35'°°° 

2.  Mean  Winding  Diameter  of  Armature.  — 

By  (30),  P-  58: 

d\  =  230  X  -    -  =  140}  inches. 

3.  Area  and  Shape  of  Armature  Conductor  ;    Size  and  Number 
of  Slots.— 

By  §  20: 

oY  =  600  X  ^-  =  278,000  circular  mils, 

o 

or 

278,000  X  -  =  219,000  square  mils. 
4 

A  bar,  -}  inch  high  by  £  inch  wide,  has  a  cross-section  of 
218,750  square  mils.  Arranging  6  such  bars  in  each  slot,  as 
shown  in  Fig.  358,  the  width  of  the  slot  is  found  -}-J-  inch,  its 
total  depth,  3^  inches,  and  the  distance  between  mean  wind- 
ing diameter  and  external  circumference  is  obtained  i-|  inch, 
hence  by  (34),  p.  70: 

«  X  .)  X  x 


. 

2    X   TT 

this  being  the  nearest  number  divisible  by  16. 


§  140]      EXAMPLES  OF  GENERA  TOR   CALCULA  TION. 

4.   Length  of  Armature  Core.  — 
By  (48),  p.  92: 


589 


5.   Arrangement  of  Armature  Winding.  — 
By  (45),  p.  89: 


One   commutator-division    per  slot   making  the  number  of 
commutator-bars  smaller  than  this  minimum,  we  have  to  take 


Fig.  358. — Dimensions  of  Slot  and  Armature  Conductors,  2OOO-KW  i6-Pole, 
Radial  Outerpole  Type,  Low-Speed  Generator. 

two  per  slot,  and  the  winding  must  be  arranged  in  772  coils  of 
3  turns  each.  "  ., 

6.   Radial  Depth,  Minimum  and  Maximum  Cross -Section,   and 
Average  Magnetic  Density  of  Armature  Core. — 

BY  (138)*  P-  201 : 


By  (48),  p.  92 : 


188,000,000 


.90 


=  61  inches, 


59°  DYNAMO-ELECTRIC  MACHINES.  [§  14O 

allowance  being  made  for  6  air-ducts  of  \  inch  width,  and  for  2 
phosphor-bronze  end-frames  of  £  inch  thickness,  thus: 

6  x  -J  -f  2  x  -J-  =  2j  inches. 

Total  radial  depth  of  armature  core : 

6J  +  3-J  =  10  inches. 
Maximum  depth  of  armature  core: 


H  -|-  io2  =  Vio*  +  io2  =  14  ii 


b\—   \     I  144  X  sin^  I  +  io2  =  Vio'  +  io2  =  14  inches. 
4 


By  (232),  p.  341: 

S&1  =  16  x  29^  X  6|  X  .9  =  2920  square  inches. 
By  (233),  p.  341: 

6"a2  =  16  X  29  J-  X  14  X  .9  =  5950  square  inches. 

P-  34i: 


/  (31,600)= 


^=  I5- 


=  10.4  ampere-turns  per  inch. 
Average  density: 

(B"a  =  58,000  lines  per  square  inch. 
7.    Weight  and  Resistance  of  Armature   Winding.  — 
(57),  P-   ioo  : 

A  =  /  i  +  .293  x  X  535°  =  12.400  feet. 


/ 


By  (58),  p.  101: 

wt&  =  .0000303  x  278,000  x  12,400  —  105425  Ibs. 
By  (61),  p.  105: 

r&  =  — ^-gi  X  12,400  X  2  ^'000=  -00183  ohm,  at  15.5°  C. 

8.   Energy  Losses  in  Armature,  and  Temperature  Increase. — 
By  (72),  p.  112: 

134  X  7t  X  io  -  336  X  3  X  \\  X  294  X  .9 

1728 
=  55  cubic  feet. 


§140]      EXAMPLES  OF  GENERATOR   CALCULATION.          59 l 

In  this  the  depth  of  the  slot  is  taken  3  inches  only,  in  order 
to  allow  for  the  volume  of  the  lateral  projections  of  the  teeth. 

Frequency: 

jVt  =  ~  x  8  —  9.33  cycles  per  second. 

By  (68),  p.  109: 

P&  =  1.2  X  37oo2  X    00183  =  30,000  watts. 

By  (73)1  P-  II2: 

Ph  =  18.1  X  9.33  X  55  =  9300  watts. 
By  (76),  p.  120: 

Pe  =  .081  X  9.332  X  55  =  400  watts. 
By  (65),  p.  107: 

/»A  —  30,000  -f-  9300  -f-  400  —  39,700  watts. 

By  (79).  P-  I25: 

SL  —  134  X  n  x  2  X  (36  +  10)  =  38,700  sq.  inches. 
Ratio  of  pole  area  to  radiating  surface : 

144!  X  TT  X  32  X  .70  _  10,200  _ 
38,700  ~  38,700 

hence  by  (81),  with  the  use  of  Table  XXXVI.,  p.   127: 


and  by  (63),  p.  106: 
r'a  =  (i  -f  .004  X  45°)  X  .00183  =   .00216  ohm,  at  6oJ°  C. 

[NOTE.  — For  the  calculation  of  the  hysteresis  loss  in  toothed 
armatures,  Dr.  Max  Breslauer1  gives  a  more  accurate  expres- 
sion, consisting  of  two  terms,  P'h  -\-  P"h  ;  the  former,  P\  ,  rep- 
resenting the  loss  in  the  solid  portion  of  the  core,  and  the  latter, 
P\  ,  the  loss  in  the  teeth  only.  While  P'h  is  obtained  from 
(73)  by  inserting  for  M  the  weight  of  the  solid  portion,  the 
second  term,  P\ ,  is  the  hysteresis  loss  in  the  teeth,  due  to 

1  "  On  the  Calculation  of  the  Energy  Loss  in  Toothed  Armatures,"  by  Dr. 
Max  Breslauer,  Elektrotechn.  Zeitschr.,  vol.  xviii.  p.  80  (February  1 1,  1897); 
Electrical  World,  vol.  xxix.  p.  325  (March  6,  1897). 


592 


DYNAMO-ELECTRIC  MACHINES. 


[§140 


the  smallest  density  (in  the  largest  section,  at  the  periphery 
of  the  armature)  multiplied  by  a  factor, 


W' 


which  depends  upon  the  ratio, 


of  minimum  to  maximum  width  of  tooth,  and  upon  the  shape  of 
the  slot,  ranging  as  follows: 


RATIO 

r(b\\ 

FACTOR  J  I  -7—  1 

b\ 

V     *  / 

h 

Rectangular 

Circular 

Slot. 

Slot. 

0 

5.00 

21.00 

0.05 

3.75 

13.00 

.1 

3.04 

8.75 

.2 

2.47 

5.34 

.3 

2.10 

3.77 

.4 

1.83 

2.90 

.5 

1.61 

2.25 

.6 

1.44 

1.81 

.7 

1.30 

1.51 

.8 

1.19 

1.30 

.9 

1.09 

1.14 

1.0 

1.00 

1.00 

The  hysteresis  loss  in  the  mass  of  the  teeth,  however,  ordi- 
narily is  only  a  small  fraction  of  the  total  hysteresis  loss,  fh, 
of  the  armature,  and  the  total  hysteresis  loss  in  well-designed 
machines  is  so  small  compared  with  the  C'^Moss  that  the  dif- 
ference in  the  total  energy  loss  due  to  the  use  of  the  above 
method  amounts  to  but  a  few  per  cent.,  and  that,  therefore,  in 
the  majority  of  practical  cases  such  a  refinement  in  the  calcu- 
lation is  unnecessary. 

Thus,  in  the  present  example,  which  is  chosen  to  illustrate 
the  above  statement,  because  in  it  the  difference  between  the 
approximate  and  the  exact  methods,  on  account  of  the  great 


§  140]      EXAMPLES  OF  GENERA  TOR   CALCULA  TION.          593 

mass  of  the  teeth — about  n  cubic  feet — is  near  its  maximum 
amount,  we  have: 

P\  =  18.1  X  9-33  X  (55  -  n)  =  745°  watts; 
Minimum  density  in  teeth: 

188,000,000  188,000,000 

3425 


(•«*-?) 


2  X  .70  X    I  144  X—  —   )  X  29£  X  .9 

=  55,000  lines  per  square  inch; 
Hysteresis  factor  for  this  density: 

rj  —  19.21  watts  per  cubic  foot. 
Ratio  of  minimum  to  maximum  width  of  tooth: 

X  *        1JL 
336  » 


•'t  •*•  T-T-    /\     "-  j 

336 

Tooth-factor,  by  interpolation  from  the  above  table: 


.  '.    P\  =  19.21  X  9-33  X  ii  X  i-53  =  3°°°  watts. 
The  total  hysteresis  loss,  therefore,  theoretically  accurate,  is 
J*h    —  7450  -|-  3000  =  10,450  watts. 

This  is  about  12^-  per  cent,  greater  than  the  value  found  on 
p.  591  (Ph  =  9300  watts),  while  the  increase  in  the  value  of  P± 
due  to  this  difference  amounts  to  about  3  per  cent,  only.] 

b.    DIMENSIONING    OF    MAGNET    FRAME. 

i.    Total  Magnetic  Flux  and  Sectional  Area  of  Frame.  — 
BY  (i56)»  P-  2I4' 

0'  =  1.15  x  188,000,000  =  216,000,000  webers. 
By  (218),  p.  339: 

216,000,000 


- 
85,000 


=  2540  square  inches. 


594 


D  YNA MO-ELECTRIC  MA  CHINES, 


[§140 


2.  Cores. — The  length  of  the  polepieces  being  32  inches 
(equal  to  length  of  armature  core),  and  their  circumferential 
width  being 

jeA 

144-f  X  sin  — —  =  20  inches, 

the  core  section  must  be  so  dimensioned  that  the  projecting 
strip  of  the  polepiece  has  the  same  width  both  in  the  lateral 


'Fig.   359. — Dimensions  of  Armature  and   Field  Magnet    Frame,    2000  KW, 
i6-Pole,  Radial  Outerpole  Type,  Low-Speed  Generator. 

and  in  the  circumferential  directions;  making  this  uniform 
width  of  the  polepiece-shoulder  3^-  inches,  see  Fig.  359,  the 
total  actual  cross-section  of  the  cores  becomes: 

•Sc.s.  =  8  X  25  x  13  =  2600  square  inches. 
Length  of  cores,  by  Table  LXXXIIL,  p.  321: 

/m  =  16  inches. 
3.   Polepieces. — 
Bore: 


</p  X  144 


2  x  -~  = 


inches. 


Distance  between  pole-corners: 

/'p  =  144!  X  sin  31°  =  8}  inches. 


§140]      EXAMPLES   OF  GENERATOR   CALCULATION.  595 

Radial  thickness,  in  centre,  lj  inch;  at  ends, 


'*  +  (72TV  -    ^SiV-  I0*)  =  21  inches. 


4.  Yoke.  —  Making  the  yoke  of  same  width  as  the  armature 
core,  its  radial  thickness  is: 

_      2540     _  g  inches. 
16  X  32 

In  order  to  secure  a  straight  seat  for  the  cores  and  to  allow 
room  for  the  flanges  of  the  magnet-coils,  bosses  of  |-j-  incn 
radial  height  must  be  provided  at  the  internal  periphery  of  the 
yoke,  making  the  external  diameter  of  the  frame,  Fig.  359, 

144*  +  2  x  (i*  +  16  +  ft  +  5)  =  191  inches. 

C.    CALCULATION    OF    MAGNETIC    LEAKAGE. 

i.   Permeance  of  Gap-  Spaces.  — 

*t  =   14433<3  U    ~  i  =  i-35  -  -25  =  LI  inch;  b\  = 
Ratio  of  radial  clearance  to  pitch: 


Product  of  field-density  and  conductor-velocity: 

35,000  X  42.8  =  1,500,000. 
By  Table  LXVII.,  p.  230: 

^,  =  3-2. 

From  Table   LXVI.,   p.  225,  for  a  corresponding   perforated 
armature, 

*«.  =  i-9- 

Average  factor  of  field  deflection: 


596  DYNAMO-ELECTRIC  MACHINES.  [§  14O 

%  (i75)»  P-  23o: 

-(i44-S  X  n  X  .70  +  1.29  X  336  X  .76)  X  \   (32    +  31) 

3    =4 * 

2-55  X  (i44|  —  144) 


2.  Permeance  of  Stray  Paths. — 
By  (181),  p.  233: 

1^06  +  2  X  13  X  16-j    =   g    x  (i6  g  +   ^  2) 

19  +  13  X  JJ 
-  248. 

From  Fig.  359 : 

3,  =  16  X  2*^132  =  16  X  9  =  144, 
From  Fig.  359: 

5   1=  8  X   (32  X  20)  -  (25  X  13)  =  8   x    I9<7  -  158. 
16 

3.  Probable  Leakage  Factor;  Total  Flux.— 
By  (157),  p.  218: 

_  3190  +  248  +  144+  158  _  3740  _ 

A.      —    —    —    ~-       —    —    I.I7- 

3190  3190 

By  (158),  p.  218: 

7d   =  1.025  X  1.17  =  1.20. 
.-.    ^'  =  1.20  x  188,000,000  —  260,000,000  webers. 

d.    CALCULATION    OF    MAGNETIZING    FORCES. 

i.   Shunt  Magnetizing  Force. — 


Air  gaps  : 

184,000,000 
atgo  =  .3133  =  -—  -  -  --  X  2.55  =  28,800  ampere-turns. 


§140]      EXAMPLES  OF  GENERATOR   CALCULATION.          597 

Armature  core: 

at      =^rf(^42ooo2ooo\  /i84,ooo,ooo\-| 

"  2  Ly  V     2920     /        \     5950     /  J 

14.5  4-  5.6 
=    ^  J    '    J   -  x  30  =  300  ampere-turns. 

|r-  +  3f 
/"a  =  i3o-J  x  TT  x  -: — £-—     +  6J  +  2  X  3i  =  3°  inches. 

Magnet  cores: 

20  x  184,000,000 


ampere-turns. 
Polepieces: 

=  Lr    /..aex.84.ooo.ooo\          /i84.ooo.ooo\-j 
2  L    y  2600  /         \     I0,200     /-• 

—  _fJ        111  x  5^  =  130  ampere-turns. 

Yokes: 

\          / 

1 84,  ooo,  ooo  \         11.20X184,000,0001  I 

v'36 


l6  X  5  X  32     /  16X8.7 

47       ".8 
=  -  -  X  36  =  1060  ampere-turns. 

the  maximum  depth  of  yoke  being: 

y    (5  4-  I)2  +  r^Y  =  8.7  inches. 


&  =  28,800  -{-  300  -}-  1410  -f  130  -f-  IQ6o 
=  3  1,700  ampere-turns. 

2.   Series  Magnetizing  Force.  — 

0  =  188,000,000  webers. 
Air  gaps  : 

188,000,000 
atg    '-  •3I33  X    -      Q         X  2.55  =  29,600  ampere-turns. 


DYNAMO-ELECTRIC  MACHINES.  [§140 

Armature  core: 


,  ooo,  ooo  \-| 

*5-  )J  x  3° 


=  10.4  x  30  =  310  ampere-turns. 
Magnet  cores: 

i.  20  X   1  88,  ooo,  ooo 


X  32  =  49  X  32 
/ 
=   1570  ampere-turns. 

Polepieces: 

i.2oX  i88,ooo,ooo\          /i. 20 X  188,000,000 


2600         /  10200 

=  27.4  X  5-J-  =  150  ampere-turns. 

Yoke: 

i.  20  X  i88,ooo,ooo\         ,  /i.  20  X  i88,ooo,ocx 


T 
)\ 


X 


16X5X32  16X8.7X33 

=  32  x  36  =  1150  ampere-turns. 

For  &"p  in  75,000  (corresponding  to/  ((B/;p)  =  27),  Table  XCI., 
P-  352,  gives 

*H  =  J-25- 
Maximum  density  in  teeth  : 

188,000,000 
|  X  .70  X  (i37i  X  TT  -  136  X  H)  X  29J  X  .9 

188,000,000 
=  —  -  =  100,000  lines  per  square  inch. 

looO 

For  this  density  from  Table  XC,  p.  350,  the  brush-lead  co- 
efficient is  found 

*»  =  -55, 

the  value  being  taken   near  the   upper  limit,   on  account  of 
the  low  conductor  velocity.     By  (250)  p.  352,  therefore: 

„,  =  Iias  x  336  x  6,x  37°°  x  -li^* 

ID  loO 

=  6000  ampere-turns. 

.  *.  AT  =  29,600  -f-  310  -f  1570  +  150  -f  1150  -j-  6000 
=  38,780  ampere-turns. 


§140]      EXAMPLES  OF  GENERATOR   CALCULATION.          599 
And  the  required  series  excitation: 

ATS&  =  38,780  —  31,700  =  7080  ampere-turns. 

6.    CALCULATION    OF    MAGNET    WINDING. 

Rise  of  temperature,  0m  ==  37^°  C.      Percentage  of  Regulating 
Resistance,  r^  =  20$. 

i.   Series  Winding.  — 

/T  =  2  X  (25  -f  13)  +  z\  X  n  —  87  inches. 
SK  =  2  X  (25  X  +   13  +  3t  X  n)  X  (16  -  *) 
=  1460  square  inches  per  core. 

Connecting  all  the  16  series  coils  in  parallel,  the  current  flow- 
ing in  each  will  be: 

/    = 


and  the  number  of  series  turns  required  on   each  core,  two 
magnets  being  in  series  in  each  magnetic  circuit, 

-    X   7080 

^e  =  -  -  =  16  turns. 
231-25 

By  (343)>  P-  400: 

*-  X  38,780  X  231.25  X  87 

*-'  ----  65  x  :      I46o  x  37r      x  (I  +  -°°4  x  37i) 

=  532,000  circular  mils. 

Using  a  iQ-wire  cable,  the  area  of  the  wire  required  is  : 

532,000 

-  =  28,000  circular  mils. 
19 

The  nearest  gauge  wire  is   No.  8  B.  W.  G.  (.165"  +  .010"), 
making  a  cable-diameter  of 

5  X  (.165  -j-  .010)  =  .875  inch. 
The  winding  depth  available  accommodates 

=  4  layers 


600  DYNAMO-ELECTRIC  MACHINES.  [§  14O 

of  this  cable;  hence  there  are  required: 

16 

-  =  4  turns  per  layer, 
4 

and  the  axial  length  of  the  series  coil  is 

4  X  .875  =  3£  inches, 
leaving  for  the  shunt  coil  a  length  of 

16  —  £  —  3j  =  12  inches. 
By  (344),  P-  400: 


T 

19 
Joint  resistance  of  all  series  coils: 


=  .000147  ohm  at  15.5'  C. 


Total  weight,  bare: 


o//se  =  16  x  16  X  —  X  19   X  .0824 

=  2910  pounds,  or  182  pounds  per  core. 

2.   Shunt  Winding.  —  Grouping  all  the  16  shunt  coils  in  series, 
the  gauge  of  the  shunt  wire  must  be: 

2     (31,700) 

A^  =  -      -  X   —  X   1.20  X  (i  4-  .004  X  37i) 
~    X540 

=  4690  feet  per  ohm. 

No.  5  B.  W.  G.  wire  (.220"  -f  .012")  has  4688  feet  per  ohm, 
and  therefore  gives  the  required  resistance. 

By  (346),  p.  400: 
Ah  =  3~-  X  1460  -  231.25"  X  .00235  X  (i  +  .004  X  37i) 

/  D 

=  730  -  143  =  587  watts. 

By  (312),  P-  383: 

•P'sb  =  587  X  1.20  =  705  watts  per  magnet. 


§140]      EXAMPLES  OF  GENERATOR   CALCULATION.          60  1 

By  (314),  P-  383: 

-  (31,700)  x  i  x  540 


^ 

Number  of  turns  in  one  layer: 

12 


=  760  turns  per  core. 


=  51; 


.232 
Number  of  layers  required: 

760  -  1  * 

-:       15. 

Winding  space  taken  up: 

15  x  .232  =  3^  inches. 
By  (315),  P-  384: 

Ah  =  51  X  15  X  —  =  5540  feet  per  core. 

Total  weight,  bare  : 

wt^  =  16  x  5540  X  .1465  =  13,000  Ibs.,  or  812  Ibs.  per  core. 

Total  resistance: 

r»h  =  16  X  5540  X  .0002128  =  18.9  ohms,  at  15.5°  C. 

By  (318),  p.  385: 

r'8h  =  18.9  X  (1.004  X  37i)  =  21.7  ohms,  at  53°  C. 

By  (317),  P-  384: 

r"sh  =  21.7  X  1.20  —  26  ohms,  entire  shunt  circuit. 

•  '  •     Ah  =  ^r  —  20.8  amperes,  shunt  current,  at  normal  load. 
20 

Actual  magnetizing  force  : 

ATse=  2  X  16  X   231.25         =     7,500  ampere-turns. 
AT8h  =  2  X  51  X  15  X    20.8  =  31,800       " 

Total  exciting  power  :       A  V  —  39,300  ampere-turns. 


602  DYNAMO-ELECTRIC  MACHINES.  [§140 

6.    CALCULATION    OF    EFFICIENCIES. 

1 .  Electrical  Efficiency.  — 
B7  (353),_  P-  406: 

n  —  ~  540  X  3700 

540  X  3700  +  (3720. 8) 2  x  .00216  -+-  3700 2  x  .000147  +  20.8 2  x  26- 

2,000.000 

—  =  .978,  or  97.8  $. 
2,043,3°° 

2.  Commercial  Efficiency. — 
By  (361),  p.  408: 

2,000,000  2,000,000 

%  = V-  -  = l =  -947>  or  94.7  #. 

2,043,300  +  9700  -\-  60,000       2,113,000 

3.  Weight- Efficiency. — 

The  weight  of  this  machine  is  estimated  as  follows: 

Armature: 

Core,  55  cubic  feet  of  wrought  iron,        .  26,500  Ibs. 
Winding    and    insulation,    connections, 

etc.,  .         .         .         .  .  12,000    " 

Commutator,  .....  15,000    " 

Skeleton  pulley,  spider  frames,  shaft,  etc.,  16,500    " 


Armature,  complete,         .         .       -.  .      .         70,000  Ibs. 
Frame : 

Magnet-cores,    16    X    13    X    25    X    16    = 

83, 200  cubic  inches  of  cast  steel,  .  23,000  Ibs. 
Yoke,  194  X  7t  x  32  X  5  =  97,500  cubic 

inches  of  cast  steel,  ....  27,000  " 
Polepieces,  16  X  20  X  32  X  ij  =  19,000 

cubic  inches  of  cast  steel,  .-  ...  5,ooo  " 
Field-winding,  spools,  and  insulation,  .  20,000  " 
Supporting  lugs,  flanges  and  bosses  on 

frame,  outboard  bearing,  etc.,      .         .      15,000    " 

Frame,  complete,     .        \         .      ••-<,-•       .         90,000  Ibs. 


[§  141      EXAMPLES  OF  GENERA  TOR   CALCULA  TION.         603 

Fittings: 

Brush-shifting  and  raising  devices,  brushes 

and  holders,  etc.,  .         .         .         .     4,000  Ibs. 

Switches,  connections,  cables,  etc.,  .      1,000    " 


Fittings,  complete,       .         .         .         ,         .       5,000  Ibs. 


Total  net  weight  of  dynamo,        .  '      .  165,000  Ibs. 

Weight  efficiency: 

2,000,000 

—  •  —  '  -  =  12.1  watts  per  pound. 
165,000 

141.   Calculation    of  a   Multipolar,  Consequent   Pole, 
Perforated  Ring,  High-Speed  Shunt  Dynamo: 

100  KW.    Fourpolar  Iron  Clad   Type.    Wrought-Iron 

Cores,   Cast-Steel   Yoke   and  Polepieces. 
200   Volts.    500  Amps.    600  Revs,  per  Min. 

(Calculation  in  Metric  Units.) 

a.    CALCULATION    OF    ARMATURE. 

i.   Length  of  Armature  Conductor.  — 
From  §15:        £  =  .70, 


From  Table  IV.,  p.  50: 

el  =  3.8  x  lo^5  volt  per  metre  per  bifurcation. 
From  Table  V.,  p.  52: 

#c  =  24  metres  per  second; 
From  Table  VII.,  p.  54: 

OC  =  3850  gausses; 
From  Table  VIII.,  p.  56: 

E  =  1.04  x  200  =  208  volts. 
By  (26),  p.  55  : 

-  2    X    208    X     I0~5 


3.8  X  .4  X  385° 


604  DYNAMO-ELECTRIC  MACHINES.  [§141 

2.    Sectional  Area  of  Armature  Conductor.  — 

By  (28),  P.  57: 

(£a)2min  =  .2    X    ^   =   50  mm.  ', 

or  by  (29)  p.  57: 

(<Unm  =  -5   X  =  8  mm. 


3.   Mean  Winding  Diameter  of  Armature,  and  Number  of  Per- 
foratio?is.  — 

By  (31),  p.  58: 

X 


Adding  to  the  diameter  of  the  armature  wire  2  mm.  radially 
for  slot-lining  and  clearance,  the  size  of  the  perforation  will  be 
12  mm.  per  conductor.  By  Table  XVI.,  p.  71,  the  depth  of 
the  slots,  for  a  machine  of  the  size  under  consideration,  may 
reach  5  cm.,  hence  the  conductors  can  be  placed  4  layers  deep. 
The  number  of  the  perforations,  by  Table  XIII.,  p.  66,  should 
be  between  100  and  150,  and  the  thickness  of  the  projections, 
by  Fig.  52,  p.  72,  should  be  from  .5  to  .9  times  the  width  of 
the  channels;  and  these  two  conditions  are  fulfilled  by  mak- 
ing the  slots  of  a  width  sufficient  for  one  conductor.  The 
number  of  perforations,  then,  is: 


4.   Length  of  Armature  Core.  —  By  §  23,  p.  76: 
.         100    X    n8          0 

4  =  -  =  33  cm' 


5.   Arrangement  of  Armature  Winding.  — 
By  (45),  P-  89: 

.  208    X    2 

(^c)min  =  -  =  42    divisions. 
IO 

The  next  larger  divisor  of  128  being  64,  the  winding  consists 
of  64  coils  of  8  conductors  each. 


§141]      EXAMPLES  OF  GENERATOR   CALCULATION.          605 

6.   Radial  Depth,  Minimum   and  Maximum  Cross  -Section,  and 
Average  Magnetic  Density  of  Armature   Core.  — 


By  (138),  P.  202: 
#  =  6-^~ 


X 


512  X  600 


By  (48),  p.  92: 


8,120,000 


10,000  X  23  X  .88 


=  10  cm. , 


the  maximum  flux-density  in   the  armature  core,  (Ba  =  10,000 
gausses,  being  taken  from  Table  XXII  ,  p    91,  and  the  ratio 


SCALE,  1:5. 


Fig.  360. — Dimensions  of  Armature,  IOO-KW  Fourpolar  Iron  Clad  Generator. 

of  magnetic  to   total  armature  section,  £3  =  .88,  from  Table 
XXIII.,  p.  94. 

External  diameter  of  armaturej  see  Fig.  360: 

d\  =  76  +  5  =  81  cm. 
Diameter  at  bottom  of  channels: 

76  —  5  =  71  cm. 
Internal  diameter  of  core: 

71 .—  2  X  10  =  51  cm. 


606  DYNAMO-ELECTRIC  MACHINES.  [§141 

Maximum  depth: 

81  x    7t  X  .70 
*'.  =  -  g  --     -  =  22.3  cm. 

By  (232),  P.  341: 

S*  =  4  X  23  x  10  X  .88  =  810  cm". 
By  (233),  p.  34i: 

Saa  =  4  X  23  X  22.3  X  .88  =  1810  cm2. 
By  (231),  p.  341: 


=  4.  i  ampere-turns  per  cm. 

Average  density: 

<Bft  =  8100  gausses. 

7.    Weight  and  Resistance  of  Armature  Winding.  — 
By  (5S)»  P-  99- 


By  §  28,  p.  101: 


X  118  =  420  m. 


t&  —  .0089  X  8a  x       X  420  =  188  kg. 
4 


By  (62),  p.  105: 

i 


—  X  420  x    (     "wx/     )  =  .0089  ohm,  at  15.5°  C. 


4X2' 

\o     x 

4 

8.   Energy-Losses  in  Armature,  and  Temperature  Increase. — 
By  (74),  P-  114: 

65.5  X  7t  X  23  X  15  X  .88  -  128  X  /  1.2  X  3-6  +  12*  - 

Ml  = 

1,000,000 

—  .0615  cbm. 

Frequency: 

600 
Nl  =  ~2—-  X  2  =  20  cycles  per  second. 


§  141]      EXAMPLES  OF  GENERA  TOR   CALCULA  TION.          607 

By  Table  XXX.,  p.  115  (&a  =  8100): 

rj  =  627.6  watts  per  cbm. 
By  Table  XXXIV.,  p.  122  (^  =  0.5  mm.): 

e'  —  2.7  watts  per  cbm. 
By  (68),  p.  109: 

JPA=  1.2  x  soo2  x  .0089  =  2670  watts. 

By  (73),  p-  112: 

A  =  627.6  x  20  x  .0615  =  773  watts. 
By  (76),  p.  120: 

A  =  2.7  X  2oa  X  .0615  =  67  watts. 
B7  (65),  P.  107: 

A  =  2670  +  773  +  67  =  3510  watts. 

By  (79),  p.  125: 


x  ,  x  2  x  (,3  +  IS  +  3x  5) 


=  20,000  cm2. 
Ratio  of  pole  area  to  radiating  surface: 

81  X  n  x  23  X  .70 

—  —  .2015. 

20,000 

From  Table  XXXVI,  p.  127: 

0'a   =   41°   C. 

By(8i),  p.  127: 

oa  =  6.45  x  41  x    35I°  =  42°  C. 

20,000 

Armature  resistance,  warm,  by  (63),  p.  To6: 

r\  =  .0089  X  (i  +  .004  x  42)  =  .0104  ohm,  at  57.5*  C. 

b.    DIMENSIONING    OF    MAGNET    FRAME. 

i.    Total  Flux  through  Magnetic  Circuit,  and  Sectional  Areas  of 
Frame.  — 

By  (156)  and  Table  LXVIII.  : 

0'  =  i.3o  x  8,120,000  =  10,500,000  webers. 


608  DYNAMO-ELECl^RIC  MACHINES. 

By  Table  LXXVL,  p.  313: 


and 


=  10.500,000  =  750cm. 
14,000 

=  .0,500,000  =      m. 

13,000 


2.  Magnet  Cores. — Each  of  the  two  magnet  cores  carries  two 

<H Z3Q™/mr» 


Fig.   361. — Dimensions  of  Field-Magnet  Frame,    IOO-KW    Fourpolar    Iron- 
Clad  Generator. 

of  the  four  magnetic   circuits,   Fig.  361,    hence   the    magnet 
diameter: 

For  a  flux  of  5,250,000  webers  passing  through  each  core, 
Table  LXXXIL,  p.  320,  gives  .75  as  the  ratio  of  length  to 
diameter,  consequently 

4»  =  -75  X  22  =  16.5  cm. 

3.  Polepieces. — The  radial  clearance  from  Table  LXI.,  p.  209, 
being  3  mm.,  the  bore  is: 

</p  =  810  +  2X3  =  816  mm. 
Pole  distance : 

/'p  =  816  X  sin  13^°  =  190  mm. 


§141]      EXAMPLES  OF  GENERATOR    CALCULATION.  609 

Pole  chord: 

h&  =  816  X  sin  31^°  =  425  mm. 
Thickness  in  centre,  22  mm. ;  at  ends, 


22 


4.  Yoke. — Only  one  magnetic  circuit  passes  through  the 
yoke-section;  fora  breadth  of  23  cm.,  equal  to  length  of  arma- 
ture core,  therefore,  the  thickness  of  the  yoke  is: 


810 

=  9cm. 


4  X  23 
Length  over  all  (Fig.  361): 

816  +  2  X  (22  +  ^5  +  90)  =  1370mm. 

Height  of  frame : 

816  +  2  X  90  =  1000mm. 

C.    CALCULATION    OF    MAGNETIC    LEAKAGE. 

1.  Permeance  of  Gap  Spaces. — 

For  z;c  X  OC  =  24  X  3850  =  92,500, 

Table  LXVI.,  p.  225,  gives 

*IQ  =   1-955 
therefore  by  (176),  p.  230: 

-(8i.6X.7  +  8i  X.8)  x  23 

<%  =  i 2200  _ 

1.95  X  (81.6  -81)  "  1.16" 

2.  Permeance  of  Stray  Paths. — 
By  (165),  p.  223,  and  (185),  p.  237: 

$  —  (T6>5  "t~  38.5)  X  (22  n  +  23  +  2  X  9)  _ 

30+   .3    X    22 

By  (196),  p.  243: 


19  +  42.5  X  ~ 


610  DYNAMO-ELECTRIC  MACHINES.  [§  141 

B)T  (204),  p.    247  : 

2  X 


l   =4X  (8  X23) 
"4  _  _  „ _, 


19.75  16.5 

3.   Probable  Leakage  Coefficient,  and  Total  Flux. — 
By  (157),  p.  218: 

1900+166+17  +  110       2193        t  1F, 

A  =  -  =:  1.1D. 

1900  1900 

By  (158),  p.  218,  and  Table  LXV.  : 

A'  =  I.04X  1.15  =1.20, 
.  • .     0'  =  1.20  x  8,120,000  =  9,750,000  webers. 

d.    CALCULATION    OF    MAGNETIZING    FORCES. 

1.  Air  Gaps. — 
Actual  density : 

8,120,000 

5C  =  -  -  —  3690  gausses; 

2200 

hence  by  (229),  p.  340: 

atg  =  .8  X  3690  x  1.16  =  3430  ampere-turns. 

2.  Armature  Core. 

By  (237),  p.  343: 


l"&  =  61  X  TT  X  6o      •   +  10  4-  2  X  5  =  51  cm- 

By  (230),  p.  340,  and  Table  LXXXIX: 

at&  =  4.  i  X  51  =  210  ampere-turns. 
3.   Magnet  Cores.  — 

(Bwi  =  •  75  ' —    =  1 2, 800  gausses. 

2    X222- 

4 
•  '  .     0*w.i.  =  13.8  X  21  =  290  ampere-turns. 


§141]      EXAMPLES  OF  GENERATOR   CALCULATION  611 

4.   Polepieces.  — 
Density  at  joint  with  cores: 

^  =  9,750,000  =12>8oogausseg; 

2    X    22°~ 

4 
Density  at  poleface: 

8,120,000 

(BP2  =  -  -  -  =  3940  gausses, 

-X  81.6  X  7t  X  23  X  .70 

By  (241),  p.  346,  and  Table  LXXXIX.  : 


/(&  \  =/(I2f8o°)  +/(394Q)=  15-2  +2-34 

J  PJ  2  2 

=  8.77  ampere-turns  per  cm. 
Corresponding  average  density: 

<Bp  =  I0>75°  gausses. 
Length  of  circuit  in  polepieces,  see  Fig.  361  : 

/"p  =  10  cm. 
.•.     «/p  =  8.77  x  10  =  90  ampere-turns. 

5.    Yoke.— 


/(n,8oo)  =  ii.  i  ampere-turns  per  cm.  ; 

^o*=    9°    cm-  (Fig-  36i); 
.«,    tf/ag>  =  1  1.  1  x  90  =  1000  ampere-turns. 

6.    Armature  Reaction.  — 

For(&p=  10,750  gausses,  Table  XCI.,  p.  352,  gives  >&14  =.1.25 
Maximum  density  in  iron  projections: 

8,120,000 
—  -  =  15,  700  gausses, 

-  X  .70  X  (72.2  X  TT  —  128  X  1.2)  X  23  X.88 

for  which  Table  XC.,   p.  350,   gives   an   average  coefficient   of 
brush  lead    of  £1S  =  .4. 


6  12  DYNAMO-ELECTRIC  MACHINES.  [§14=1 

Hence  by  (250),  p.  352: 


at,  =  ,.,5  X  .  x  2400  ampere-turns. 

7.    70/tf/  Magnetizing  Force  Required.  —  Summing  up  we  have: 

AT  =  3430  -f-  210  -j-  290  -j-  90  -f-  1000  -f-  2400 
=  7420  ampere-turns. 

e.    CALCULATION    OF    MAGNET    WINDING. 

Temperature  increase  desired,  0m  =  35°  C.  ;  percentage  of 
regulating  resistance,  at  normal  load,  rx  —  50  per  cent,  of 
magnet  resistance. 

Table  LXXX.,  p.  317,  gives  for  a  20  cm.  multipolar  type 
magnet  core  a  ratio  of  winding  height  to  core  diameter  of  .36, 
which  makes  the  winding  depth  for  the  present  case: 

^m  =  -36  X  22  =  8  cm., 
and  therefore  the  mean  length  of  one  turn: 

/T  =  (22  -f  8)  X  n  =  94.25  cm. 

Hence  by  (318),  p.  385,  if  the  two  coils  are  connected  in 
series,  each  taking  100  volts, 


x     r  x  '-5°  x  (I  +  -°°4  x  35) 

=  119.5  metres  per  ohm. 

According  to  the  common  millimetre  wire  gauge,  a  wire  of 
a  specific  length  of  122  metres  per  ohm  has  a  diameter  of 
3m  =  1.6  mm.,  bare,  ortf'm  =  1.6  -\-  .25  =  1.85  mm.,  covered. 
This  wire  will  give  the  required  temperature  increase  with 

50  X  122 

~        ~~  53  per  cent 


extra-resistance  in  circuit. 
Radiating  surface: 


=  (22  +  2  X  8)  X  n  x  (16.5  -  .5)  =  1910  cm8. 


$141]      EXAMPLES  OF  GENERATOR   CALCULATION.          613 
By  (314),  p.  384: 


2IO 

Number  of  turns  possible  per  layer: 

•|J  "       'V=8 

Number  of  layers  required: 


- 
86 

Net  winding  depth  needed  : 

#m  =  4i  X  1.85  =  76  mm. 

By  (315),  p.  384: 

Zsh  =  86  x  41  X  9          =  3320  m. 


.  '.     >'ah  =  —  —  =  27.2  ohms,  per  coil,  at  15.5°  C. 

By  (318),  p.  385: 

r'8h  =  27.2  X  (i  +.004  X  35)  =  31.0ohms,atso.5°  C. 

By  (31?),  P-  384: 

''"sh  =  2  X  31.0  x  1.53  =  94.8  ohms,  total  resistance  of 
shunt  circuit. 

•  *«     ^sh  =  —  ^  =  2.11  amperes. 

Actual  magnetizing  force  : 

^7"=86X4i  X  2.  ii  =  7440  ampere-turns. 
Weight  per  coil,  bare: 

wtsh  =  ^x  17.8  =59  kg., 

IOOO 

17.8  being  the  weight,  in  kilogrammes,  of  1000  metres  of  cop- 
per wire,  of  1.6  mm.  diameter. 


CHAPTER  XXX. 

EXAMPLES   OF    LEAKAGE    CALCULATIONS,    ELECTRIC    MOTOR 
DESIGN,    ETC. 

142.  Leakage    Calculation    for    a    Smooth   Ring,  One- 
Material  Frame,  Inverted  Horseshoe  Type  Dynamo : 

9.5  KW  "Phoenix55  Dynamo.1 
105  Yolts.    90  Amps.    H20  Revs,  per  Min. 

a.   PROBABLE  LEAKAGE  FACTOR     (FROM  DIMENSIONS  OF 
MACHINE). 

i.  Permeance  of  Air  Gaps. — From  Fig.  362,  which  shows  the 
principal  dimensions  of  this  machine,  its  gap  area  is  obtained: 

I     /  TO.&    V     TT  II2°\ 

Sg  =  -l-  -f-iif  x  7t  X  —fa  1  X  9  =  I25  square  ins. 

The  useful  flux  (see  below,  §  142,  <£.,  i,  p.  616): 

$  =  2,600,000  webers, 
therefore  the  field  density: 

X"  =  --  °°>ocg  —  20,800  lines  per  square  inch. 

The  conductor  velocity  being 

ii  x  7t        1420 

«/-  =  -       —  X  -         =68  feet  per  second, 
12  60 

the  product  of  density  and  speed  is 

3C"  X  f'c  =  20,800  X  68  =  1,415,000, 

for  which  Table  LXVL,  p.  225,  gives  a  factor  of  field  deflec- 
tion:   £12  =  1.30. 


1  Silvan  us   P.    Thompson,   "  Dynamo-Electric    Machinery,"  fourth  edition, 
p.  416  and  Plate  V. 

614 


§142]        EXAMPLES  OF  LEAKAGE   CALCULATION. 
Hence,  by  (167),  p.  226: 

2   _  L£5 __  J^5_ 

"    1.30  X  (n|  -  lof)       .975  " 

2.    Stray  Permeances.  — 

By  (177)1  p-  232: 


"Tk 


Fig.  362. — 9.5  KW  Phoenix  Dynamo. 


By  (192),  p.  241: 
10  X  9 


6J  +  10  X  I 


The  projecting  area  of  the  yoke,  at  each  core  is 

/6i         \ 
S  =  [    „    -h  2  )  x  9  =  47.25  square  inches, 


hence,  by  (202),  p.  246, 

$    =  I7-2!  _|_  _     _9_X  4| 
8*          8}  +  (6  4-  4* 


=  5-4  +  2.5  =  7.9. 


6i6  DYNAMO-ELECTRIC  MACHINES.  [§142 

3.   Probable  Leakage  Factor. — 
BY  (i57),  P-  218: 

\         I28  +  9.6  +  io.6  +  7.9_  156.1  _ 

A  — —       — —   —   1,44, 

128  128 

b.    ACTUAL    LEAKAGE    FACTOR    (FROM    MACHINE    TEST). 

1.  Total  Magnetizing   Force   of  Machine. — The    dynamo    is 
compound-wound,  having  a  series  resistance  of  .021  ohm,  and 
a  shunt  resistance  of  39.76  ohms:  its  armature  resistance  is 
.04  ohm.     Therefore,  the  total  current  generated: 

/'  =  90  -|-      -^r-  =  92.65  amperes, 

and  the  total  E.  M.  F. : 

E'  =  105  -j-  92-65  X  .04  -|-  90  X  .021  =  1 10.6  volts. 

There  are  180  conductors  on  the  periphery  of  the  armature, 
hence  by  (138),  p.  202: 

,        6  X  110.6  X  io9 

9  =  =  2,600,000  webers. 

1 80  X  1420 

The  magnet  winding  consists  of  108  series  and  3454  shunt 
turns,  and  the  two  series  coils  are  connected  in  parallel,  the 
two  shunt  coils  in  series  to  each  other,  consequently: 

AT^  —  1 08  X  —  =  4860  ampere-turns, 

2 

and 

ATsh  =  3454  X  2.65  =  9140  ampere-turns; 

making  the  total  actual  exciting  power: 

AT  —  4860  +  9140  =  14,000  ampere- turns. 

2.  Magnetizing  Force  Required  for  Magnet  Frame. — 
By  (228),  p.  340: 

atg  =  .3133  X  20,800  X  .975  =  6350  ampere-turns. 

B7  (230),  P-  34o: 

at&  =  91  x  ii-J  =  1050  ampere-turns, 


§142]         EXAMPLES  OF  LEAKAGE   CALCULATION.  617 

the  average  specific  magnetizing  force  being: 

f  ((&"a)  —  f  (100,000)  =  91  ampere-turns  per  inch, 
and  the  length  of  the  path  in  the  armature  core: 

l\  =  9A  X  n  X  ^-^  +  i A  -  "4  inches- 
B7  (250),  P-  352: 

afr  =  1.56  X  -       X292'53  X  ~  ~  2460  ampere-turns, 

the  factor  1.56  corresponding  to  a  poleface  density  of 

/(($>" p)  =  -  =  26,000  lines  per  square  inch. 

n-f  x  7f  x~y^  x  .9 

360 

Hence,  magnetizing  force  left  for  field  frame: 
atm  —  14,000  —  (6350  -\-  1050  -j-  2460)  —  4140  ampere-turns. 

3.  Total  Magnetic  Flux  ;  Actual  Leakage  Factor. — The  mag- 
net frame  is  entirely  of  cast  iron;  the  path  length  in  the  same 
is  (Fig.  362): 

''m  =  2  x  (8f  +  5)  +  6£+  3  X  ^   =37-7  inches, 
and  the  mean  area  of  it  is: 

5m  =  33  X  7  X  9  +  4-7  X  9»  X  9  =  66  squafe  inches 

Inserting  these  values  into  (209),  p.  259,  we  obtain: 

,  /$'\      4140 
f  \~—  I—  —   — =no  ampere-turns  per  inch. 


According  to  Table  LXXXVIII.,  p.  336,  this  specific  mag- 
netizing force  corresponds  to  a  magnetic  density  in  highly 
permeable  cast  iron,  of 

0' 
<S>"m  =  — ^  =  50,000  lines  per  square  inch. 


6i8 


D  YN A  MO-ELECTRIC  MA  CHINES. 


[§143 


from  which,  by  formula  (210),   p.  259,   follows  the  total  mag- 
netic flux: 

0'  —  66  X  50,000  =  3,300,000  webers. 

The  actual    leakage   coefficient,   consequently,   from   (214), 
p.  262,  is: 


. 

2,600,000 

The  probable  leakage  factor  computed  from  the  dimensions 
of  the  frame  has,  on  page  616,  been  found  A  =  1.22,  which  is  4 
per  cent,  below  the  actual  value. 

143.  Leakage   Calculation    for    a    Smooth   Ring,  One- 
Material  Frame,  Double  Magnet  Type  Dynamo  : 

40  KW  "  Immisch  "  Dynamo.1 
690  Yolts.    59  Amps.    480  Revs,  per  Min. 

a.   Probable  Leakage  Factor.  —  (From  Fig.  363). 


Fig.  363. — 4O-KW  "  Immisch  "  Dynamo. 

By  (167),  p.  226: 


i-3  X  (25^  -  24) 


1.95 


1  For  data  of  this  machine  see  Gisbert  Kapp's  "  Transmission  of  Energy, 
third  edition,  p.  272. 


§143]         EXAMPLES  OF  LEAKAGE    CALCULATION.  619 

By  (194),  p.  242: 

4  +  l6)  X  TO  +  4  X  16        16  X  7t    .    2X161 

24  f9i+7-T      9f     J~ 

__  267  -f-  85         352    __ 

A,    —    —     —  —  -    —  —    •—  —  —  -   —   A  •  »>  4  • 
207  207 

<£.   Actual  Leakage  Factor.  — 

The  armature  is  wound  with  760  turns  of  No.  9  B.  &  S.  wire, 
resistance  .36  ohm;  the  field  winding  consists  of  984  series 
turns  (No.  4  S.  W.  G.)  per  core,  two  coils  in  parallel,  joint 
resistance  .25  ohm. 

By  (9),  P-  37: 

E'  —  690  -J-  59  (.36  -f-  .25)  =  690  -f-  36  =  726  volts. 

By  (138),  p-  202: 

6  X  726  X  io9 

#   =  -  —  -  =  12,000,000  webers. 

760  X  480 


By  (139)'  P-  202: 


=  23,100  lines  per  square  inch. 


By  (228),  p.  339: 

atK  =  .3133  X  23,100  X  1.95  =  14,  100  ampere-turns. 
By  (232),  p.  341: 

5a,  =  2  X  (16  —  2)  X  4j  X  .865  =  109  square  inches  (54 
square  inches  per  side  being  given). 

By  (233),  p.  341: 


S&,  -  2  X  (16  -  2)  X  4i  X  |-       -  i  X  .865 

=  230  square  inches. 
By  (231),  p.  341: 

,  ™  ,    __   /(IIO,000)   +/(52,200)   _  290   -f    10.2 

=  150  ampere-turns  per  inch. 


620  DYNAMO-ELECTRIC  MACHINES.  [ 

By  (236),  P.  343: 

l\  =  19-1  x  TT  X  9°\^  +  4i  =  22f  inches. 

By  (230),  p.  340: 

#/a  =  150  x  22f  =  3400  ampere-turns. 

The  angle  of  lead  was  measured  to  be  about  20°,  therefore 
bY  (25°),  P-  352: 

atr  =  1.40  X  760  X  —  X  -^  =  3500  ampere-turns. 

The  total  magnetizing  force  of  the  machine  is: 
AT  =  984  x     -  =  29,000  ampere-turns. 

The  frame  is  all  wrought  iron,   having  a  uniform  cross-sec- 
tion of 

Sm  —  10  x  1  6  =  1  60  square  inches, 
and  the  length  of  each  circuit  in  the  frame  is: 

I'm  —  75  inches. 
Hence  we  have: 


75  X-  ~     =  29'°°°  ~~  l1^100  +  34oo  -f  3500) 

=  8000  ampere-turns, 


from  which: 

.  /   $>'  \       8000 
/  *  —  —  I  = 


=  106.  7  ampere-turns  per  inch. 


Consulting  Table  LXXXVIIL,  p.  336,  we  find: 

0' 

——  =  102,000  lines  per  square  inch; 
1  60 

or,  the  total  flux  : 

$'  =  160  x  102,000  —  16,400,000  webers. 

.-.  A  =  16'400'000^  1.36. 

12,000,000 

The  probable  leakage  factor  found,  in  this  case,  is  about  3 
per  cent,  smaller  than  the  actual  one. 


§144]         EXAMPLES  OF  LEAKAGE    CALCULATION.  621 

144.  Leakage  Calculation  for  a  Smooth  Drum,  Com- 
bination Frame,  Upright  Horseshoe  Type 
Dynamo: 

200  KW  "  Edison  "  Bipolar  Railway  Generator.1 
500  Volts.    400  Amps.    450  Revs,  per  Min. 

<7.   Probable  Leakage  Factor. — (From  Fig.  364). 


<-  

•35"-  —  y 

^BEDPLATE 

OPPOSITE  FIELI3S  =  625  8Q.   INS. 


Fig.  364. — 200-KW  "  Edison  "  Bipolar  Railway  Generator. 
By  (167),  p.   226: 

-  (  23}  X  n  +  25^  X  7t  X  ^i  )  X  34| 
4\  «">/ 


1.30  x 

By  (178),  p.  232: 


2    X     I2J    +    1.5    X    25 


-    23f) 


= 


2.52 


1  For  description  see  Electrical  Engineer,  vol.  xiii.  p.  321  (March  23,  1891); 
Electrical  World,  vol.  xix.  p.  220  (March  26,  1892). 


622  DYNAMO-ELECTRIC  MACHINES.  [§144 

By  (188),  p.  239: 

I  f34lX  (2o|  +  - -X  26)  +625! 

$3=^-  _J  =  6o.9. 

2  X  71 

By  (i99)»  P-  245: 

24=345  +  -  341  X  26_         _=I6<5< 

2  X3'  +  (26  +  2i)x  - 
By  (157),  p.  218: 
i     _  451  +  38-7  +  60.9  +  16.5  _  567.1  _ 

4~^~  isr: 

&   Actual  Leakage  Factor.  — 

The  total  E.  M.  F.  generated,  by  considering  the  losses  in 
armature  and  series  field  windings,  is  found:  E'  —  520  volts; 
and  there  are  228  conductors  on  the  armature  periphery;  there- 
fore by  (138),  p.  202: 

.        6  X  520  X  io9 

228  X  450       =  3o,5oo,ooo  webers. 

-?o,  500,000 

.  •.     3C  =  -  —  =  27,000  lines  per  square  inch. 

H35 

By  (228),  p.  339: 

afg  =  .3133  X  27,000  X  2.52  =  21,300  ampere-turns. 
By  (232),  p.  341: 

SAl  —  2  x  34j  X  8f  x  .85  =  502  square  inches. 

By  (233),  P-  34i : 

S.a  =  2  X  34l  X  8f  x  y  *-jjk  -  i  X  .85  =  665  square  ins. 

By  (231),  p.  341: 

/(<»'.)  =  I -[/  (60,500)  +/(45?70o)]^I3>2  +  8-6 

=  10.9  ampere-turns  per  inch. 
By  (236),  p.  343: 

^  =  i5i  X  7f  X  9°  +2^  +  8|  -  23.9  inches. 


§144]        EXAMPLES  OF  LEAKAGE   CALCULATION.  623 

BY  (230),  P-  34o: 

at&  =  10.9  X  23.9  =  260  ampere-turns. 

By  (250),  p.  352: 

AOO    -4-     3.6  2^4; 

at,   =,.ISX.I4X  7       "X^ 

—  7000  ampere-turns. 

The  magnet  winding  consists  of  about  8000  shunt  turns  and 
of  46  series  turns.  The  shunt-circuit  has  a  resistance  of  139 
ohms,  making  the  shunt  field  current  at  normal  load 

500 

78h  =  3—  =  3.6  amperes; 
«5y 

hence,    the   total   magnetizing   force    actually    exciting    th  ; 
machine  at  full  load: 

AT  —  8000  X  3.6  -|-  46  x  400  =  47,200  ampere-turns; 
and  by  (207),  p.  258: 

atm  =  47,200  —  (21,300  -j-  260  +  7000)  =  18,640  ampere-turns. 
The  section  of  the  cores  is: 

•Sin  =  252  X  -  =  490.9  square  inches; 
4 

and  that  of  the  yoke : 

Sy  =  25  x  21  —  525  square  inches; 

the  resultant  area  in  wrought  iron,  therefore,  can  be  taken  at 
about  *S"w.i.  —  5°°  square  inches. 

The  cross-section  at  centre  of  polepieces  is: 

34i  X  "-J  =  405  square  inches, 
and  the  vertical  cross-section  is: 

34^  X  26  =  885  square  inches. 

Increasing  the  minimal  area  by  one-third  of  the  difference 
between  the  maximum  and  minimum  area,  we  obtain: 

,   885  -  405 
•Sc.i.  =  405  +  -  " ~      =565  square  inches, 

O 


624  DYNAMO-ELECTRIC  MACHINES. 

which  we  will  take  as  the  resultant  area  of  the  circuit  in  cast 
iron. 

The  lengths  of  the  magnetic  circuit  are: 
in  wrought  iron,  /"w-i.  =  120  inches;  in  cast  iron,  /"c>i  =36  inches. 

By  (213),  p.  261,  we  consequently  have  the  equation: 


I2°  X  /  +        X 

which  is  satisfied  by 

$'  =  37>5oo»°oo> 

for,  by  inserting  this  value  of  #',  we  obtain: 


=  120  X  /  (75>°°°)  -f  36  X  /  (66,300), 

and  with  reference  to  Table  LXXXVIII.,  p.  336,  this  becomes: 
120  x  24.7  -f-  36  x  436  =  2960  -f  15,700  =  18,600, 

which  is  practically  identical  with  the  actual  number  of  ampere- 
turns. 

Hence,  the  actual  leakage  factor: 

A  =  37,500,000  =  t  33 

30,500,000 

In  this  instance,  the  probable  value  obtained  is  about  2^2 
per  cent,  in  excess  of  the  actual  value. 

145.  Leakage   Calculation   for  a  Toothed   Ring,  One- 
Material  Frame,  Multipolar  Dynamo  : 

360   KW  "  Thomson-Houston  "   Fourpolar   Railway 

Generator.1 
600  Yolts.    600  Amps.    400  Revs,  per  Min. 

a.   Probable  Leakage  Factor.  —  (From  Figs.  365  and  366). 
Effective  total  length  of  armature  conductor: 

Ze  =  90  X  4  X  ^  x  '-^If-  =  683  feet. 


1  This  machine,  but  bored  for  a  48-inch  armature,  is  used  in  the  power 
station  of  the  West-End  Railway  Company  of  Boston,  Mass.;  for  description 
see  Electrical  Engineer,  vol.  xii.  p.  456  (October  21,  1891). 


§145]         EXAMPLES   OF  LEAKAGE    CALCULATION.  625 

Conductor  velocity: 


v  =  (44i^:  ij-i)X 

12 

The  total  E.  M.  F.  is 


x          =  74-  *5  feet  per  second. 


Figs.  365  and  366. — 36o-KW  Thomson-Houston  Fourpolar  Railway 

Generator, 
hence,  by  (144),  p..  205: 

3C"  =  — =  34,000  lines  per  square  inch. 

72  x  683  X  74-25 

.  •  .     7>c  X  3C"  =  74.25  X  34>000  =  2,520,000. 

Ratio  of  radial  clearance  between  armature  and  field  to  pitch 
of  slots: 


therefore,  by  Table  LXVL,  p.  225:     £12  =  2.0,   and  by  Table 
LXVII.,  p.  230:     £13  =  4.6;  average:    k^  —  3.3. 


Hence,  by  (175),  p.  230: 

T  [45  X  7t  +  (1.24  +  .094)  X  90]  X 


82' 


_  4 


1 80 


X  25 


3-3  X  (45  ~44i) 


626  DYNAMO-ELECTRIC  MACHINES.  [§145 

By  (181),  p.   233: 


ii  X  -  —  h  J4  X 
2 


9 
=  69-5  +  43  =  112.5. 

By  (197),  p.  243: 


=  132-5- 

_  858  +  112.5  +  132-5  _  "°3  _  ,  -8< 
•     •    A  -  '"858"  -   858  - 

Ratio  of  width  of  slot  to  pitch : 

It   :    i-553  =  -523- 

for  which  Table  LXV.,  p.  219,  gives  a  factor  of  armature 
leakage  of 

A,  =  1.04; 

hence  the  total  probable  leakage  coefficient: 
A'  =  1.04  x  1.285  =  1.34, 

b.   Actual  Leakage  Factor.  — 

The  machine  is  compound-wound,  having  19,200  shunt  am- 
pere-turns and  66.00  series  ampere-turns  on  each  magnet;  the 
total  exciting  power  per  circuit,  two  coils  being  magnetically 
in  series,  therefore,  is: 

AT  =  2  X  (19,200  -j-  6600)  =  51,600  ampere-turns. 
By  (228),  p.  339: 

a*g  =  -3X33  X  34, o°°  X  1.65  =  1 7, 600  ampere-turns. 
By  (232),  p.  341: 

5ai  =  4  X  9f  X  25  X  .85  =  828  square  inches. 


§145]         EXAMPLES  OF  LEAKAGE   CALCULATION.  627 

By  (233),  p.  341: 

S**  —  4  X  2  -  X  25  x  .85  =  1252  square  inches. 

By  (231),  p.  341: 

f  it**  \  -  f  (62,500)  +  /  (41,  200)  _  14.2  -f  7-8 

/  ^  *>    ~~  ~~  2 

=  11  ampere-turns  per  inch. 
By  (236),  p.  343^ 

T+'" 

/"a  =  3'i  X  n  X    —      ---  h  9l  +  2  x  i  J  =  26J  inches. 


,  P- 
#4  =  ii  X  26  J  =  300  ampere-turns. 

The  shunt  current  is  16   amperes,   and  the  angle   of  brush 
lead,  by  measurement,  about  5°,  hence  by  (250),  p.  352: 

616         5° 

atv  =  2  x  360  x  -    -  X  -^5-  =  3100  ampere-turns. 
4          loo 

The   magnetizing   force    left   for   the   magnet    frame,  con- 
sequently, is: 

atm  =  51,600  —  (17,600  -f-  300  -}-  3100)  =  30,600  ampere-turns. 

The  magnet  frame  is  of  cast  iron;  each  circuit  has  a  length 
of  l"m  —  90  inches;  the  total  cross-section  of  the  cores  is: 

2  X  22  X  25  =  1  100  square  inches, 
and  that  of  the  yokes: 

4  x  i2|-  x  25  =  1250  square  inches. 
Taking 

S"m  =1125  square  inches 

as  the  resultant  sectional  area,  we  have: 


628  DYNAMO-ELECTRIC  MACHINES.  [§  146 

-  /  #'  \         30,600 
/I  —      1=       * =  340  ampere-turns  per  inch; 

$' 

—  62,500  lines  per  square  inch; 

$'    =  1125  X  62,500  =  70,500,000  webers. 
The  useful  flux  is : 

,        2  x  6  X  620  X   io9 

0  =  =  51,600,000  webers; 

360  X  400 

consequently: 

A'=  7°'f°'000=1.37. 

51,000,000 

The  formulae  for  the  probable  leakage  factor,  for  this  ma- 
chine, gave  a  value  2\  per  cent,  below  this  actual  figure. 

146.  Calculation  of  a  Series  Motor  for  Constant  Power 

Work: 

Inverted  Horseshoe  Type.    Toothed-Drum  Armature. 
Wrought-Iron   Cores   and   Polepieces,   Cast- 
iron  Yoke. 
25  HP.    220  Yolts.    850  Revs,  per  Min. 

a.    Conversion  into  Generator  of  Equal  Electrical  Activity.  — 

Assuming  a  gross  efficiency  of  90  per  cent.,  and  an  electrical 
efficiency  of  91  per  cent,  (see  Table  XCIX.,  p.  422),  the  elec- 
trical energy  active  in  the  armature  of  the  motor  is,  by  (382), 
p.  420: 

pl=  746  x  25  =  20^800watts> 

and  the  E.  M.  F.  active,  by  (383),  p.  421 : 

E'  =  220  x  .91  -  200  volts; 
hence,  by  (384),  p.  421,  the  current  capacity: 

20,800 
7  :     ~^o~~    =  104  amperes, 

which,  in  the  present  case  of  a  series  motor,  is  also  the  current 
intensity  to  be  suppled  to  the  motor  terminals. 


§146]  EXAMPLES  OF  MOTOR   CALCULATION.  629 

Intake  of  motor,  by  (381),  p.  420: 


b.   Calculation  of  Armature.  — 

According  to  §  146,  a,  the  armature  has  to  be  designed  to 
give  a  total  E.  M.  F.  of  200  volts  and  a  total  current  of  104 
amperes,  at  a  speed  of  850  revolutions.  For  the  reason  ad- 
vanced on  p.  63,  a  toothed  armature  with  its  projections 
highly  saturated  at  full  load  is  chosen.  In  order  to  obtain 
high  efficiencies  at  small  loads,  the  armature,  as  explained  in  § 
116,  must  overpower  the  field,  and  therefore  a  low  conductor 
velocity  and  a  small  field  density  must  be  taken: 

fti  =  .75;       e  =  62.5  x  io~8  volt;        vc  =  40  feet  per  second; 

3C"  =  20,000  lines  per  square  inch. 
BY  (26),  p.  55: 

^-£•421   -=400  feet. 
62.5  X  40  X  20,000 

By  (27),  p.  57: 

tfa2  —  300  x  104  =  31,200  circular  mils. 

2  No.  8  B.  &  S.  (.128"  -|-  .016")  have  2  X  16,510  =  33,020  cir- 
cular mils  area. 

By  (30),  P.  58: 

d\  =  230  X  ~j^  =  xo-j-f  inches. 

Approximate  size  of  slot,  by  Table  XV.,  p.  70: 

r  x  w  . 

12  No.  8  B.  &  S.  wires,  arranged  in  6  layers  (see  Fig.  368) 
with  .020"  slot-lining  give  a  slot, 


Making  the  pitch  ^  inch,  the  number  of  slots  is  obtained, 
Fig.  367: 

,        n|  X  TT 
»«•=       *-r~     =  74- 


63°  DYNAMO-ELECTRIC  MACHINES. 

Hence,  by  (40),  p.  76: 


146 


_  400  X  12 
74  X  6 


=  10J  inches; 


and  by  (138),  p.  202: 


Figs.  367  and  368.  —  Dimensions  of  Armature  Core,  25-HP  Inverted 
Horseshoe  Type  Series  Motor. 

making  the  maximum  density  in  the  teeth  at  full  load: 

a*        _  3,180,000 
t  —  ~~/  -  —  \~  — 

(  9JTr^  ~  ti  )  X  74  X  io|  X  .90  X  -75 

V      74  /  2 

=  130,000  lines  per  square  inch. 
The  shape-ratio  of  the  armature  core  is: 


therefore  by  Table  XXIV.,  p.   96: 

Lt  =  2.90  X  400  =  1160  feet; 


whence: 


and 


=  .00000303  X  33,020  X  1160  =  116  Ibs. 


X  1 1 60  X  .000626  =  .092  ohm,  at  15.5°  C. 


4X  2 


§146]  EXAMPLES  OF  MOTOR   CALCULATION.  631 

c.   Energy  Losses  in  Armature,  and  Temperature  Increase.  — 
Shaft  diameter,  by  (123),  p.  185: 


internal  diameter  of  discs: 

3£  inches. 

Sai  —  (9!  —  3^)  X  i  of  X  .90  =  61.7  square  inches. 
,Sa2  =  uj-  x   ioj-  X  .90  =  113.5  square  inches. 

io         -1 


—  7.5   ampere-  turns  per  inch 
Average  density: 

<B"a  =  40,000  lines  per  square  inch. 
By  (72),  p.  112: 

(-X  (nf  +  3i)  X  TT  X  4i-74X  if  Xfi)xio|X  .9 

M  =  li-  --  Z  - 

1728 

—    .427  cubic  inch. 

JV^  =   |  —  =  14.  2  cycles  per  second. 
60 

By  (68),  p,  109: 

P&  —  1.2  X  io42  x  .092  :=  1194  watts. 
By  (73),  P-  12: 

A  =  n-55  X  14-2  X  .427  =  7°  watts. 
By  (76),  p.  120: 

/*,  =  .046  X  14-  22  X  .427  =  4  watts. 

By  (65),  p-  107: 

/>A  =  1194  +  70  4-  4  =  1268  watts. 
By  (78),  p.  125: 

^  =  i  if  X  n  X  [ioj  +  1.8  X  (.5  X   n|  +  2  X 
=  913  square  inches. 


632  DYNAMO-ELECTRIC  MACHINES. 

Ratio  of  pole  area  to  radiating  surface  : 

ii  j  X  7t  x  io|  X  .75 
~~ 


[§146 


for  this  ratio,  and  for  vc  =  40  feet  per  second,  Table  XXXVI., 
p.  127,  gives: 

6'a  =  44°  C., 


hence  ea  =  44  X  ~  =  61°  C. 

.-.      r'&   =  .092  x  (i  -{-  .004  X  61)  —  .115  ohm,  at  76.5°  C. 
d.   Dimensioning  of  Magnet  Frame. 

In   order  to  secure  a  small  excitation,  the  density  in  the 
wrought  iron  is  taken: 

®"w.i.  —  75>°°°  lines  per  square  inch; 

'  T"1 


Fig.   369. — Dimensions  of  Magnet  Frame,  25  HP  Inverted  Horseshoe  Type 

Series  Motor. 

and  that  in  the  cast  iron: 

(fc"ci    —  30,000  lines  per  square  inch. 

0'  =  1.20  x  3,180,000  =  3,820,000  webers. 

3,820,000  .     , 

£wi    —  _  —  51  square  inches. 

75,000 


§146] 


EXAMPLES  OF  MOTOR   CALCULATION. 

=  137  square  inches. 


633 


Cross-section    of   cores,  rectangle,  5^"  X    5^",  between  two 
semi-circles  of  5^"  diameter;  (Figs.  369  and  370)  : 

5i  X  5i  +  5i2  X  —  =  50.5  square  inches. 


Fig-  37°- — Joint  of  Magnet  Core  and  Yoke,  25  HP  Inverted  Horseshoe  Type 

Series  Motor. 

Length  of  cores,  by  Table  LXXXIII.,  p.  321 : 
4i  =  7J  inches. 

Cross-section  of  yoke:  15"  X  8J"  (=  127.5  square  inches). 
Core  projection,  rectangular:   loj  x  2-J  X  8J. 
Area  of  contact  of  same  with  yoke,  Fig.  370: 

(lof  4-  2  x  2|)  x  81  -j-  5^5  =  160  square  inches. 
Polepieces: 

</p  =  nj  -j-  2  x    TV  =  1 '  J  inches. 

/'p  =  n|  X  sin  22^°  —  4}  inches. 
e.  Calculation  of  Magnetic  Leakage. 
Width  of  tooth: 

**  =  ^  "  »  -  -5  -  -328  =  .172  inch. 


Ratio  of  radial  clearance  to  pitch : 

-T  ='125' 

Product  of  field  density  and  conductor  velocity: 
3C"  X  vc  =  20,000  x  40  =  800,000. 


634  DYNAMO-ELECTRIC  MACHINES.  [§146 

i  P-   227: 

-  (n|  X  n  X  -75  +  x-5   X  .172  X  74  X  .88)    x    iof 


36  X   (nl~ 

120 

Ts  =  2S7' 


By  (17°),  p-  228: 

v  =  (9|X*-74Xfi)  x   iofx 
By  (171),  p.  228: 

*»  =  74  X.  75x1*^2*  =  ,09 

By  (168),  p.  227: 

_  257  X  (1370 


257  +  1370  +  209 
By  (179)  p.  232: 

:  2X6     +  2  x  6  +  1.5  X^5i  =  3'5 
By  (192),  p.  241: 


it  n 

3  X  -         4i  +  6|  X  - 

2  2 


By  (202),  p.  246: 

_  iof  X  6|-5o.5  icj  x  8 

—  —  '- 


1  -  =  3+4.3  =  7. 


I.  12. 


_    221    -f-  9.8  +  8.3   +   7.3  246.4 

A.     —    -  - 

221  221 

K  =  1.05  x  1.12'=  1.18. 
/.  Calculation  of  Magnetizing  Forces. 

tg     =  .3133  X  20,000  x  -45  =  2820  ampere-turns. 
4     =  7-5  X  12  —  90  ampere-turns. 


§146]  EXAMPLES  OF  MOTOR   CALCULATION.  635 

#/w  j   =  24. 7  X  40  =  190  ampere-turns. 
atci    =50  x  iii  —  590  ampere-turns. 

2  I  oO 

A  T    =  2820  -f-  9°  +  I9°  H-  59°  +  2530  =  7000  ampere-turns, 
g.  Calculation  of  Magnet   Winding. 

The  total  magnetizing  force  being  kept  exceedingly  low,  a 
very  small  winding  depth  will  be  sufficient  to  accommodate 
the  winding.  Taking  hm  =  i  inch,  formula  (291),  p.  374,  will 
give  the  mean  length  of  one  turn: 

4     =  2  X  5i  +  (Si  -f  J)  X  TT  =  31  inches. 

JV8e  = =  135  turns,  total,  or  68  turns  per  core. 


Zse    =  6S  X  3I  =  176  feet  per  core. 


[_5i  X  r- 


=  2  X  7i  X5i  X  r-~+  i     x7r=:253sq.  in.  p.  magnet. 


For  a  rise  of  20°  C,  we  find: 

'-  =  ~  X  *ff  X  I+<<x;4Xao  =  -0231  ohm  per  core. 
=  7620  feet  per  ohm. 


.0231 


The  nearest  gauge  wire  is  No.  2  B.  W.  G.  (.284"  -f  .020"), 
with  a  specific  length  of  7813  feet  per  ohm.  The  number  of 
turns  of  this  wire  filling  one  layer  on  the  cores  is: 


.284-]-.  020       "     .304 

therefore,  the  number  of  layers  required: 

^=3. 

23 

Actual  winding  depth: 

^'m  =  3  X  .304  —  .912  inch. 
Actual  excitation: 

:2X23X3X52   =  7176  ampere-turns. 


636  DYNAMO-ELECTRIC  MACHINES.  [§146 

Joint  series  resistance,  warm: 

>•»   =  '~~  X  (i  +  .004  X  20)  =  .0125  ohm,  at  35.5°  C. 
Total  weight  of  wire,  bare: 

wt^  —  2  X  23  X  3  X    3--  X  .244  =  87  Ibs. 

h.   Speed  Calculations.  — 
E.  M.  F.  lost  in  armature  and  series  winding: 

104  X  (.115  +  -0125)  =  13  volts. 
Actual  E.  M.  F.  active  in  armature: 

E'  =  220  —  13  =  207  volts. 

(Spare  magnetizing  force  being  provided,  this  increase  does 
not  affect  the  above  calculations.) 
Torque,  by  (93),  p.  138: 

T  —     -  --;0-    X  104  X  444  X  3,180,000  =  172.5  foot-lbs. 
Specific  generating  power: 

e"  =   —  -L  -  =  14.6  volts  at  i  revolution  per  second; 
550 

hence,  by  (389),  p.  426,  the  speed  at  any  supply  voltage,  E: 


.  =  60  X  -  8.52  X     - 


i4-  14. 

=  4.11  E  -  54. 

For  E  =  220  volts:   JV9  —  904  —  54  =  850  revs,  per  min. 
"    E  =  200  volts:  Nz  =  822  -  54  =  768  revs,  per  min.,  etc. 

/".    Calculation  of  Efficiencies. 
Electrical  efficiency,  at  normal  load: 


=  aoo  X   .Q4-(..I5  = 

200    X     104 

Commercial  efficiency  at  normal  load: 

_  200  X  104  -  (iQ4a  X  .1275  +  74  +  i5°°) 
200  X   104 

-  20,800  —  (1380  4-  1574)  _  17,846  _ 

20,800       ~  20,800   •80 


§147]  EXAMPLES  OF  MOTOR   CALCULATION.  637 

Commercial  efficiency,  at  J  load  (the  energy  loss  in  arma- 
ture and  series-field  windings  varying  practically  as  the  square 
of  the  load,  and  hysteresis  and  friction  losses  being  independ- 
ent of  the  load): 


X  -.800  -  [(|y  X  .380  +  I574] 


_ 
y  -  15,600  =  .85. 

-  X   20,800 
4 


Commercial  efficiency,  at  ^  load: 


^x  20,800  -  [YM   x  1380  +  1574] 


i  .  10,400 

-  X  20,800 

2 


-   =.88. 


Commercial  efficiency,  at  J  load  : 


-  X  20,800  -  f(  -  )     X  1380  +  1574! 

n,^-  !i±£  '=1540 

i  5200 

—  >X  20,800 
4 

Commercial  efficiency,  at  50  per  cent,  overload: 

_  ij  x  20,800  -  (i.52   x    1380  +   1574)  _  26,526 

4  X   20,800  '31,200   " 

The  latter  is  lower  than  the  efficiency  at  normal  load. 

147.   Calculation  of  a  Shunt  Motor  for  Intermittent 

Work: 
Bipolar  Iron  Clad  Type.    Smooth  Ring  Armature. 

Cast-Iron  Frame. 
15  HP.    125  Yolts.    1400  Revs,  per  Min. 

a.    Conversion  into  Generator  of  Equal  Electrical  Activity.  — 
Table  XCIX.  gives: 

P'  =  12,600  watts. 
By  Table  VIII.  : 

E'  =  125  —  .06  X  125  =  117.5  volts. 


638  DYNAMO-ELECTRIC  MACHINES.  [§147 

Current  in  armature,  at  full  load,  by  (384),  p.  421 : 

T,        12,600       -g^~ 
/ '  =  -        -  =  107  amperes. 
ii?-5 

Intake,  by  (381),  p.  420: 

^  =   12,600  =  1 

b.    Calculation  of  Armature. — 

In  this  case  we  want  a  weak  armature  of  few  ampere-turns 
and  a  strong  field  with  large  exciting  power.  Hence  the  con- 
ductor velocity  and  the  field  density  must  both  be  taken  very 
high: 

/#,   =  .80;  e  —.  65  x  i o~8  volt  p.  ft.;  VG  =9 2. 5 'feet  p.  second; 
3C"  =  26,000  lines  per  square  inch. 

Xi  =  .     "7-5  X  "?'—  =  76feet. 
65  X  92.5  X  26,000 

tfa2  =  250  x  107  =  26,800  circular  mils. 

2  No.  11   B.  W.  G.  (.120"  -f-  .016")  have  a  sectional  area  of 

6\  =  2  x   14,400  =  28,800  circular  mils. 

02.  C 

d a  =  230    x          L  =  15.3  inches. 

By  Table  IX.,  p.  59: 

<4  —  J5-3  X  .98  =  15  inches. 

Allowing  i\  inches   for  50  division   strips   of.  15"   width,    we 
have: 

conductors 


.  I2O  -j-  .Ol6  .  136 

per  layer. 
-  =  ftj  inches. 


§147]  EXAMPLES  OF  MOTOR   CALCULATION.  639 

//a  =  3  x  /i  +  /I/-1-  --  i  \  =  9  inches. 
)  =  /  (io7,500)  +/(36,ooo)  _  190  +  6.7 


=  98.4  ampere-turns  per  inch. 
Average  density: 

&"a  =  101,000  lines  per  square  inch. 

2  x  (6f  +  3)+i  X  * 
A;  —  63  -  X  7°  —  233 

8  * 

^4  =  233  X  2  x  .0436  =  20|  Ibs. 
ra  =  —  ^—  X  233  x  .00072  =  .021  ohm,  at  15.5°  C. 

c.   Energy  Losses  in  Armature,  and  Temperature  Increase.  — 

_.        12  X  7t  X  6-f  X  3  X  .85 
M  -.  ~"~"  =  >355          C 


-Wj  =     r      =  23.33  cycles  per  second. 

PA  —  1.2  X  io72  X  .021  =  290  watts. 
A  =  5°-8  X  23.33  X  -355  =  363  watts. 
A  =  -295  X  23.332  x  .355  =  57  watts. 
/>A  =  290  -f  363  -f  57  =  710  watts. 
,9A=  2  x  12  x  TT  X  (6|  -f  3  +  4  x  i)  =  780  sq.  inches. 

e-  =  42  x  7^  =  38°  c- 

r\  —  .021   X  (i  +  .004   x  38)  =  .024  ohm,  at  53.5°  C. 
d.   Dimensioning  of  Magnet  Frame.  — 

#'  =  1.15  x  3,500,000  =  4,025,000  webers. 

^m  =  4'°225>^°°  —  95  square  inches. 


Breadth  of  cores: 


|f  =  15  inches. 
°t 


640  DYNAMO-ELECTRIC  MACHINES.  [§147 

Breadth  of  polepieces: 

15!  X  sin  72°  =  15  inches. 

These  two  dimensions  being  equal,  no  separate  polepieces  are 
required,  and  the  frame  may  be  cast  in  one  piece,  as  shown 
in  Fig.  371. 


Fig.  371. — Dimensions  of  Armature  Core  and  Field-Magnet  Frame, 
I5-HP  Bipolar  Iron-Clad  Type  Shunt  Motor. 

e.   Calculation  of  Magnetizing  Forces.  — 
afe  —  .3133  X  26,000  x  1.4  X  |  =  7120  ampere-turns, 
at&  —  98.4  x  14  =  1380  ampere-turns. 
afm  =  101  x  85  =  8500  ampere-turns. 


atr  =  i. 80  x   -  [—  X  ^g-  =  1400  ampere- turns. 

AT  —  7120  +  1380  +  8500  +  1400  —  18,400  ampere-turns. 

f.    Calculation  of  Magnet  Winding.  — 

Since  the  motor  is  not  intended  for  continuous  work,  a  high 
increase,  0m  =  40°  C.,  is  permitted.  Regulating  resistance,  at 
full  load,  rx  =  23  per  cent. 

Height  of  winding  space,  estimated:  2-J-  inches. 

/T  =  2  (6f  +  15)  +  2\  x  7t  —  50  inches. 


§147]  EXAMPLES  OF  MOTOR   CALCULAl^JON.  641 

18,400          150 
Ash  =    -f~-  X   ~    X   1.23  X  (i  +  -004  X  40) 

=  874  feet  per  ohm, 

corresponding  to  No.  13  B.  W.  G.  (.095"  -j-  .010"). 
5M  =  2  x  (6|  -f  15  +  2|-  TT)  X  2  x  8i  =  1000  sq.  inches. 

/"8h  =  —  X  1000  x  1.23  =  655  watts. 


Number  of  turns  per  layer: 

8* 


.095    -|-    .OIO 

Number  of  layers  required : 


=  80; 


-  22. 


80 

Depth  of  magnet  winding: 
h'm  =  22  x  (.095  -+-  .010)  =  2.S2  inches. 
Z8h  =  2  x  80  x  22  x  -5^  =  14,650  feet. 

^sh  =     g         =  16  75  ohms,  shunt  resistance,  at  15.5°  C. 

r'*.  =  16.75  X  (i  +  -004  X  40) 

=  19.4:5  ohms,  shunt  resistance,  at  55.5°  C. 

^8h     =      19-45      X      1.23 

=  23.9  ohms,  res.  of  entire  shunt-circuit,  at  full  load. 
/Sh  =  -  -  =  5.23  amperes,  shunt  current,  at  normal  load. 

*3*  V 

Total  actual  magnetizing  force: 

AT  =  2  x  80  x  22  x  5.23  —  18,400  ampere-turns. 
Total  weight,  bare: 

wt^  =  l6'75  =  400  Ibs.,  or  200  Ibs.  per  core. 
.0419 


642  DYNAMO-ELECTRIC  MACHINES.  [§147 

g.   Speed  Calculations.  — 
E.  M.  F.  consumed  by  armature  winding: 

107  x  .024  =  2.6  volts. 
E.  M.  F.  active  in  armature: 

E'  -  125  -  2.6  =  122.4  volts. 
Torque  : 

r  ^  -i^-  x   107  x  H4  X  3.500,000  ==  63.3  foot-pounds. 
Specific  generating  power: 


I4OO 

Speed,  at  any  voltage,  E  : 

•0>4 


,  =  60  x  -  8.5a  x 


*5.63-3)  =  H. 


For  E  -  125:  N^  —  1428  -  28  =  1400  revs,  per  minute. 
11  E  =  110:  Nz  —  1256  -  28  =  1228  revs,  per  minute. 
"  E  =  100:  N^  =  1142  —  28  =  1114  revs,  per  minute. 

h.   Calculation  of  Current  for  Various  Loads.  — 
Current  for  full  load,  by  (392),  p.  428: 


T,  _  125  -  1/125*  -  4  X  .024  X  (746  X  15  +  200°) 

2  x  .024 
=  107  amperes. 

Current  for     load : 


125  —  A/  125*  -  4  X  .024  X  (746  X  15  X  -  +  2000) 

/'  = K * 

2    X    .024 

=  40  amperes. 
Current  for  £  load : 

125  -  A /  i252  —  4  X  .024  x  (746  X  15  X  -  +  2000) 

/'    =     -  L: 

2     X     .024 

=  63  amperes. 


§147]  EXAMPLES   OF   MOTOR   CALCULATION.  643 

Current  for  £  load  : 

I25  ~  /t/T252  -  4  X  .024  x  (746  X  T5  X   ~  +  2000) 
j<  _  _  r  __  4  _ 

2    X    .024 

=  86  amperes. 
Current  for  25  per  cent,  overload: 


I,  _  125  -      i2—  4  X  .024  X  (746  X  15  X   TJ  +  20Qo) 

2    X    .024 

=  126  amperes. 
Current  for  50  per  cent,  overload  : 


/'  —  I25  ~      »25a  —  4  X  .024  X  (746K  15  X   ij  +  2OO°) 

2  X  .024 
—  159  amperes. 

Current  for  maximum  commercial  efficiency,  by  (393),  p.  429: 


=  .1/537+2000  +  /535V  _ 
.024  \I25/ 


535        ^ 

I25 


from  which  follows  that  the  maximum  commercial  efficiency  is 
obtained  at  about  five  times  the  normal  load. 

Current  for  maximum  electrical  efficiency,  by  (394),  p.  429: 


_  MS   =  U6ampereS) 


.024       y  125          125 

which  corresponds  to  about  i£  times  the  normal  load. 

/.    Calculation  of  Efficiencies.  — 
Electrical  efficiency,  at  normal  load: 

-  I22-4  X  107  --  107'  X  .024  —  5.23*  x  19.45 

122.4  x  107 
=  13.  ,00  -,75  -535  =  ij^oo 

13.100  ^3,100 

Commercial  efficiency,  at  normal  load  : 

=  I22-4  X  107  -  (107°  X  .024  +  535  +  352  + 

13,100 

•33  ?•»• 


DYNAMO-ELECTRIC  MACHINES.  [§148 

Commercial  efficiency  at  }  load: 

=  122.4  X  86  -  (86a  X  .024  +  2887)  7455  71 

122.4  X  86  "  10,520 

Commercial  efficiency  at  £  load: 

_  122.4  X  63  -  (632  x  .024  +  2887)       _  4738 
^2.4  X  63  ~  ffc 

Commercial  efficiency  a<-  J  load: 

_  122.4  X  40  —  (4Q2  X  .024  +  2887)      _  1975       _ 
122.4  x  40  ~  4900 

Commercial  efficiency  at  25  per  cent,  overload: 

__  122.4  X   126  -  (126*  X  .024  -f  2887)  _  12,153   _    7Q 
122.4  X  126  15,420 

Commercial  efficiency  at  50  per  cent,  overload: 


=  I22'4  X  159  -  (i599  X  .024  +  2887)  __  16,006 

122.4  x  159  19,500 

In  this  case  the  efficiencies  at  overload  are  higher  than  the 
normal  load  efficiency. 

148.  Calculation  of  a  Compound  Motor  for  Constant 

Speed  at  Varying  Load  : 
Radial  Outerpole  Type.    4  Poles.    Toothed  Ring 

Armature.    Cast-Steel  Frame, 
75  HP.    440  Tolts.     500  Revs,  per  Min. 

a.  Conversion  into  Generator  of  Equal  Electrical  Activity.  — 

P'  =  60,000  watts  (by  Table  XCIX.,  p.  422). 
E1  =  440  —  .045  x  440  =  420  volts. 

,       60,000 
/    =  -         •    =  143  amperes. 

420 

b.  Calculation  of  Armature.  — 

/?,   =  .70;  e  —  55  x  To~8  volt  p.  ft.  ;  vc  =  65  feet  p.  sec.  ; 
3C"  =  30,000  lines  per  square  inch. 

=     ,  X  420  X   io-     = 

55  X  65  x  30,000 
tfaa  =  400  x  143  =  57,200  circular  mils. 


§148]  EXAMPLES  OF  MOTOR   CALCULATION.  645 

4  No.  ii  B.  W.  G.  wires  (.120"  -|-  .016"),  have  an  actual  area  of: 

4  x  14,400  =  57,600  circular  mils. 

d\  =  230  x   ~    =  2$$  inches. 


For  this  diameter,  Table  XV.,  p.  70,  gives  a  slot  of 
1  1  X  TV  inch;  actual  slot  for  36  No.  n  B.  W.  G.  wires,  see 
Fig.  372,  is  1-J--J-  inch  deep  and  -J|  inch  wide. 


Fig.  372. — Dimensions  of  Armature-Slot,  75  HP 
Fourpolar  Compound  Motor. 


Number  of  slots: 


n'   = 


X 


~S5  X  "    =  9i  inches. 


s  vy 

112    X     ' 

4 


6  X  2  X  420  X  io9  _ 


112  X  9  X  500 

10,000,000 


=  10,000,000  webers. 


=    137  +  7-6 


=  72.3  ampere-turns  per  inch. 


646  DYNAMO-ELECTRIC  MACHINES.  [§148 

Average  density  : 

(&"a  =  96,000  lines  per  square  inch. 
Z,  =  1*J£*  +  »»Jl_'.tt.><_?  x  II2  X  9  =  ^540  feet. 

o//a  =  2540  X  4  X  .0436  =  442  Ibs.  bare  wire. 

r&  =  -        -  X  2540  X  .000717  =  .114  ohm  at  15.5°  C. 
4X4 

*-.   Energy  Losses  in  Armature,  and  Temperature  Increase.  — 

M  =  (27   X  TT  X  4TV  "  TH  X  H  X   112)  X  9i  X  .875 

1728 
=  1.44  cubic  foot. 

Nl  =    ^     X  2  ==  16.67  cycles  per  second. 

P&  —  1.2  X   H32  X  .114  =  2800  watts. 

/>h  =  46.85  X   16.67  x  1.44  =  1120  watts. 

Pe  =  .0665  X   i6.672  X  1-44  =  30  watts. 

P^  —  2800  -f  1  1  20  4-  30  =  3950  watts. 

5A  =  27  x  7t  x  2  X  (9j  :  +  2|-f-  i|^  x  TT  =  3000  square  inches. 

6.  =  41   X  39S°  =  54<>  C. 

3000 

r'&  =  .114  X  (i  +  .004  X  54°)  =  .139    ohm,  at  69^°  C. 

d.   Dimensioning  of  Magnet  Frame.  —  (Fig.  373.) 

#'  -  1.20  x  10,000,000  =  12,000,000  webers. 
Width  of  frame  (equal  to  length  of  armature  core)  :  9J  inches. 
Breadth  of  cores: 

12,000,000 

-  =  8  inches. 
2  X  80,000  X  9i 

Thickness  of  yoke: 

12,000,000 


4        80,000  X  9t 
Length  of  cores: 

^m  =  7|  inches. 
Breadth  of  polepieces: 

^P  =  3Tf  X  sin.  314°  =  16|  inches. 


§  148J  EXAMPLES  OF  MOTOR   CALCULATION.  647 

Distance  between  pole-corners: 

/'p  —  31}  x  sin  13!°  •=  7|  inches. 

e.  Calculation  of  Magnetizing  Forces.  — 
The  E.  M.  F.  at  no  load  being, 

E0  —  440  volts, 
and  that  at  full  load  being 

E'  —  440  —  143  X  .139  X  1.25  =  415  volts, 

the  shunt  winding  is  to  be  calculated  to  supply  the  total  mag- 
netizing force  necessary  to  produce  440  volts,  and  the  series 


Fig.  373- — Dimensions  of  Magnet  Frame,  75  HP  Fourpolar  Compound 

Motor. 

winding,  in  order  to  regulate  for  constant  speed  at  all  loads, 
must  provide  the  difference  between  the  magnetizing  forces 
required  for  440  and  415  volts,  respectively,  and  must  be  con- 
nected so  as  to  act  in  opposition  to  the  shunt  winding.  Dif- 
ferential winding. ) 

'  Magnetizing  Force  Required  at  No  Load : 

rt         6  X  2   x  440  X  ie>9 

vP0  — =  10,  =?oo,oco  webers. 

112  x  9  X  500 

TP//  2  x  440  X   To8 

3C0  =-  -=  29,500  lines  p.  sq.  m 


72  x 


3C"o  X  f'c  =  29,500  X  65  =  1,920,000. 


648  DYNAMO-ELECTRIC  MACHINES.  [§148 

Ratio  of  clearance  to  pitch: 


112 

From  Table  LXVIL,  p.  230:  £ia  =  5.25. 

atgo  =  .3133  X  29,500  x  T3g-X  5.25  —  9100  ampere-turns. 

i       r    /         10,500,000        \        /         10,500,000         \  ~j 
at&0  =  -  X  |^/  L4  x  9*  X  2|  X  .875J  +     \ 4  X  9i  X  7i  X  .875^  J 

-  /("Q»ooo)  +/ (42,5°o)  v    _      _  29Q  +8 

—    p\    ^u  —  —  —   p\    z\j 

2  2 

=  2980  ampere-turns. 

«'m.  =/( I'^^/g0T5;°7!r±:)  x  60  =/ (83,000)  x 


=  36.1  x  60  —  2170  ampere-turns. 
.*.     AT0  —  9100  -f  2980  -|-  2170  =  14,250  ampere-turns. 

Magnetizing  Force  required  at  Full  Load.  — 

9  =  i_X  ,  X  4-5  XJ.£  =  9,900,000 webers. 

112  X  9  X   500 

JC"  =  29,500  x  -  -  =  27,800  lines  per  square  inch. 
44° 

afg  =  .3133  X  27,800  x  A-  X  5.0  =  8150   ampere-turns. 

/  (103, 700)  4-  /  (40,000)                    122. 5  +  7-S 
at&  =  y— ^ — — — '— }    J  v     ' ^  X  20  =  °    '    y  J  X  20 

2  2 

=  1300  ampere-turns. 
a*m  =/ (7^,300)  X  60  =  29.2  x  60  =  1750  ampere-turns. 

atr  =  1.25  x  112  X  9  X    —  X  >4°  ^  I3^  -  1350 amp. -turns. 

4  loo 

.'.     AT  —  8150  -f-  1300  -f-  1750  +  1350 
=  12,550  ampere-turns. 

Magnetizing  Force  for  Series  Differential  Winding. — 

ATse  —AT  -  ATse=  12,550  -  14,250  =  -  1700amp.-turns. 


§148]  EXAMPLES  OF  MOTOR   CALCULATION.  649 

As  seen  from  the  above,  the  armature  reaction,  by  increas- 
ing the  excitation  needed  for  full  load,  in  a  motor  reduces  the 
difference  between  full  load  and  no  load  magnetomotive  force; 
and  by  properly  adjusting  the  magnetizing  forces  required  for 
the  various  portions  of  the  magnetic  circuit,  the  difference  be- 
tween the  ampere-turns  required  to  overcome  the  reluctances 
of  the  circuit  at  no  load  and  full  load,  respectively,  can,  indeed, 
be  brought  within  the  amount  of  the  armature  reactive 
ampere-turns,  so  that  no  series  winding  at  all  is  needed  for 
regulation,  the  armature-reaction  (which  may  have  to  be  made 
extra  large  for  this  purpose)  taking  its  place.  [In  the  present 
machine,  this  can  be  achieved  by  increasing  the  radial  depth 
of  the  armature  core  from  2%"  to  3^",  whereby  the  average 
specific  magnetizing  force  is  reduced  to/((B"ao)  =  29.5  ampere- 
turns  per  inch  at  no  load  and  to  /((B"a)  =  23.5  ampere-turns 
per  inch  at  full  load,  making  the  corresponding  magnetizing 
forces  tf/ao  —  59°  ampere-turns  and  at&  =  470  ampere-turns, 
respectively.  Substituting  these  figures  for  those  in  the  above 
calculation,  the  total  exciting  power  at  no  load  is  found 
AT0  =  1 1, 860  ampere-turns,  and  at  full  load  AT  —  11,720 
ampere-turns;  the  remaining  small  difference  of  140  ampere- 
turns  can  easily  be  taken  care  of  by  slightly  enforcing  the 
armature-reaction,  either  by  widening  the  polepieces,  or  in 
giving  the  brushes  a  somewhat  greater  backward  lead;  and  we 
have  then  a  self-regulating  shunt-motor  of  practically  constant 
speed  for  all  variations  of  load.] 

f.    Calculation  of  Magnet  Winding. 
Series  Winding. — 

1700 

Nm  = •  =  12  turns  per  magnetic  circuit, 

H3 

or  6  turns  per  core. 

Allowing  1000  circ.  mils  per  ampere,  and  taking  2  cables  of   7 
wires  each,  the  size  of  each  wire  is: 

<J2ai  = =    10,200    circular  mils, 

or  No.  10  B.  &  S.  (.102"). 


65°  DYNAMO-ELECTRIC  MACHINES.  [§148 

Assuming  hm  —  4  inches,  twelve  cables  of  3  x  (.102"  -j-  .008") 
=  .33  inch  diameter  will  just  fill  the  winding  space,  and  but 
one  layer,  axially,  is  therefore  required. 

/T  =--  2  x  (8  +  9|~)  +  4  x  n  ='471  inches, 

wt^  —  12  x  14  X    —    X  .0315  =  21  Ibs.  per  pair  of  cores, 

or  42  Ibs.  total. 
rse  =  12  x    — -  X  -    -  —  .0034  ohm  per  pair  of  magnets,   at 


Shunt  Winding.  — 

Forfim  =  25°  C., 

Connecting  all  four  shunt  coils  in  series,  the  potential  across  a 
pair  of  coils  is  220  volts,  and  the  size  of  the  wire  required: 


=  409  feet  per  ohm, 
which  is  the  specific  length  of  No.  16  B.  W.  G.  wire   (.065"  -f- 

.007"). 

Allowing  J"  of  the  length  of  the  core  for  width  of  bobbin 
flanges,  the  radiating  surface  of  one  pair  of  shunt  coils  is: 

Su  =  2  X  (8  +  94  +  4  X  ?f)  X  2  X    (7i  --  i) 
=  870  square  inches. 

An  =  ^    X    870  —  i432  x  .0034  X  (i  +  .004  X  .25) 

/  D 

=  290  —  77  =  213  watts. 
^'Sh  =  213  x  1.45  =  309  watts. 


Allowing  %  inch  for  the  series  winding  and  its  insulation,  the 
length  available  for  the  shunt  winding  is  6J  inches,  which  holds  : 

-i-  =   94  No.  1  6  B.  W.  G.  wires; 


£148]  EXAMPLES  OF  MOTOR   CALCULATION.  651 

hence,  the  height  actually  occupied  by  the  shunt  winding: 


2  X  94 


x  .072  =  54  x  .072  —  3.89  inches. 


wtsh  =  2  x  94  X  54  X          X  .0128  —  512  Ibs.  per  pair  of  mag- 

nets, or  1024  Ibs.,  total. 
=  4  X  94X54X47*  =  1%  Qh        tota,   at         „  c 

12    X   409 

r'sh  =  196-  X  (i  +  -004  X  25°)  =  215.5  ohms,  at  40.5°  C. 

r"8h  =  215.5  X  1.45  =312  ohms,  entire  shunt-circuit,  at  full 
load. 

78h  =  -    -  =  1.41  ampere,  shunt  current,  full  load. 

Actual  magnetizing  force  at  full  load: 

AT=  2  X94  X  54  X  1.41  -  12  X  143  =  14,300-  1720 

=  12,580  ampere-turns. 

g.   Speed  Calculations.  — 

Actual  counter  E.  M.  F.  of  motor  at  full  load: 
E'  —  440  —  143  x  (.139  +  .004)  =  440  —  20%  =  419|  volts. 
Useful  flux  at  full  load  : 

$  =  10,000,000  webers. 
Useful  flux  at  no  load  : 

$o  =  10,500,000  webers. 
Torque,  at  full  load  : 

T  =  1LZ4  x    143  X   .008  x  I 

Torque,  at    no    load    (energy  for   overcoming   frictions   esti- 
mated at  P0  =  5000  watts)  : 

X  5-522-x  "X  10,500,000  =  71foot-lbs. 

2 


Specific  generating  power,  at  full  load  : 

1008 
e      =  10,000,000  X  -----  X  io~8  =  50.4  volts, 


652  DYNAMO-ELECTRIC  MACHINES.  [§149 

at  no  load  : 

1008 
r0  —  10,500,000  x  -         Xio     =  52.9  volts. 

Speed,  at  full  load  : 

^  =  60  X      419i  -  8.52  X  (.*39 


=  60  X  (8.34  —  .0405)  =  498  revolutions  per  minute. 
Speed,  at  no  load  : 


60  X  -  8.52  X 


. 
\52-9  52-9 

=  60  X  (8.32  —  .0031)  —  500  revolutions  per  minute. 

The  difference  in  speed  at  full  and  no  load  being  only  2  rev- 
olutions per  minute,  the  condition  of  constant  speed  is  fulfilled. 

149.  Calculation  of  a  Unipolar  Dynamo  : 

Cylinder  Single   Type.    Cast-Steel   Frame.    Cast-Iron 

Armature. 

300  KW,    10  Yolts.    30,000  Amps.    1000  Beys. 
per  Min. 

a.  Diameter  of  Armature,  Dimensioning  of  Frame,  and  Cur- 
rent Output.  — 

By  (423),  P.  447: 

<4  =  400  X   A/  -  =  40  inches. 


The  minimum  diameter  for  the  given  voltage,  by  (395),  p. 
438,  would  be: 

<4  =  3-45  X  10  =  34^  inches, 
which  would  correspond  to  a  maximum  speed  of 

2002 

N  =  .33  x  -  =  1333  revolutions  per  minute. 

The  dimensions  of  the  machine,  by  §  118,  are  (see  Fig.374): 
Length  of  field,  by  (409),  p.  444: 

/p  =  .3  x  40  =  12  inches. 


§  149]  EXAMPLE   OF   UNIPOLAR  DYNAMO. 

Radial  thickness  of  armature,  by  (412),  p.  445: 

£a  =  .  2  x  V^Q  —  \\  inch. 
Radial  distance  of  poles,  by  (413),  p.  445: 

£P  =  .25  X  ^40"  =  IJinch. 


653 


Fig.   374.  —  Dimensions  of  300  KW  Unipolar  Cylinder  Dynamo.     10   Volts. 
30,000  Amps.     1000  Revs. 

Height  of  winding  space,  by  (411),  p.  444: 

hm  =  .1  X  40  =  4  inches. 
Length  of  winding  space,  by  (410),  p.  444: 

4,  =  •  i25  X  4°  =  5  inches. 

Thickness  of  yoke  part  of  frame,  opposite  inner  surface  of 
exterior  shell,  by  (414),   p.  445: 

by  =  .14  x  40  —  -042  X    ^40  =  5|  inches. 

Thickness  of  frame  opposite  bottom  of  winding  space,  by 
{415),  p.  445: 


bm  =  .175  X  40  +  .055  X       ^o    =  7|  inches. 
Radial  thickness  of  outer  shell,  by  (416),  p.  446  : 
//y  =  .125  x  40  —  .03  x  ^40  =  43-  inches. 


654  DYNAMO-ELECTRIC  MACHINES.  [§149 

Radial  thickness  of  inner  shell,  by  (417),  p.  446: 

hc  =  .26  X  4°  +  -23  X  1/40   —  12  inches. 
Total  length  of  frame,  by  (418),  p.  446: 

/F  =  .625  X  40  =  25  inches. 
Length  of  magnetic  circuit  in  frame,  by  (419),  p.  446: 

I"m  —  1.2  x  40  =  48  inches. 
Current  capacity,  by  (428),  p.  448: 

/'  =  125  x  V4oi~=  30,600  amperes. 

b.  Calculation  of  Magnetizing  Forces. — 
By  (435).  P-  45° : 

at^  —  750  X  V4o    =  4740  ampere-turns. 

By  (436),  P-  45°: 

,    at&  =17.6  X  A/40  =no  ampere-turns. 
By  (437),  P-  45°  : 

atm  =  53  X  40  =  2120  ampere-turns. 
Total  magnetizing  force : 

A  71  =  4740  -J-  no  -|-  2120  =  6970  ampere-turns. 

c.  Calculation  of  Magnet  Winding.  — 
By  (438),  p.  45*: 

/T  =  2.83  x  40  -  -785  X  ^40  —  108  inches. 
By  (439),  P -451- 

Sx  =  .39  x  4Q2  —  -i  X  t/4or  =  600  square  inches. 
By  (440),  P-  45 1: 

wtm  =  .0074  x  403  —  .002  x  1/40*  =  453  Ibs. 

By  (329),  P-  390: 

[/,  loS^v2 

31.3  X  (M7o  X   —\ 

om  —   —  

453  -'  -004  X  [31.3  X  (6.970  X  9)*  X  ^ 

=  _I5i4"D 
453  -  61.6 


§150]  EXAMPLE   OF  MOTOR   GENERATOR.  655 

Size  of  wire,  for  20  per  cent,  extra  resistance: 

Ash  =  "7o^  x  9  x  I>2°  x  (r  +  -°°4  x  39^ 

=  8718  feet  per  ohm,  or  No.  .1  B.  W.  G.  (.300"  -f  .020"). 
Number  of  wires  per  layer: 

5  -  2  x .  JL  =  15. 


.320 

Number  of  layers: 

±1   ' '  =  12. 

.320 

Total  length : 

Zsh  =  15  x  12  X  9  =  1620  feet. 
Resistance: 

rsh  =  1620  x. 0001147  =  .186  ohm,  at  15.5°  C. 

r'8h  =  .186  X  (i  +  .004  X  39i°)  =  .215  ohm,  at  55°  C. 

r"9h  =  .215  x  1.20  =  .254  ohm,  entire  shunt-circuit. 

I O ' 

/sh  =.  -  -  =  39.4  amperes. 
•  254 

Actual  excitation: 

AT  —  15  x  12  X  39.4  =  7080  ampere-turns. 

d.    Weight- Efficiency. 

The  weight  of  this  machine,  complete,  will  be  in  the  neigh- 
borhood of  10,000  Ibs.,  thus  making  its  weight-efficiency  about 
30  watts  per  pound.  , 

150.  Calculation  of  a  Motor-Generator : 

Bipolar  Double   Horseshoe   Type.     Cast-Steel  Frame, 

Toothed  Ring  Armature. 
5J  KW.    1450  Revs,  per  Min. 

Primary:  500  Volts,  11  Amps.    Secondary:  HOTolts, 

44  Amps. 

a.   Ratio   of  Armature   Turns  ;  Current  Output  of   Secondary 

Winding. 

Electromotive  forces  active  in  armature: 

E\  =  500  —  .064  x  500  =  468  volts, 
E   =  no  -+-  .064  x   no  =  117  volts, 


656  DYNAMO-ELECTRIC  MACHINES.  [§  150 

Ratio  of  number  of  armature  turns: 

N^  =  Q  ^  468  =  ^ 

Electrical  activity  in  primary  winding: 

^  x  /',  =  468  X  ii  =  5150  watts. 
Current  intensity  of  secondary  winding: 

/'   =  5  5    =  44  amperes. 
117 

b.   Calculation  of  Armature. — 

fti  =  .75;  e  =  62.5  x  io~8  volt  p.  ft. ;  vc  =  67^  feet  p.  sec.; 
3C"  =  25,000  lines  per  square  inch. 

The  relation  of  the  two  windings  being  fixed  by  the  ratio  of 
the  E.  M.  Fs.  active  in  the  same,  it  is  only  necessary  to  cal- 
culate one  of  them.  For  the  primary  winding  we  have: 

468  X  io8 

—  444  feet. 


62.5  x  67^  x  25,000 

tfai2  =  382  X   ii  =  4225  circular  mils, 

or  No.  16 B.  W.  G.  (.065"  +  .015"  =  .080"). 

Arranging  24  of  these  wires  in  8  layers  of  3  each,  the   depth 
of  the  slot  is  obtained: 

//a  =  8  X  .080  -j-  .012  4-  .035  =  .687",  or  fj-  inch;  and 
its   width: 

bs  =  3  x  .080  4-2  X  .012  =  .264",  or  -JJ  inch 

d'&  =  230  X   —  *-  =  10H  inches; 

145° 

d"&  =  lofj-  +  -H-  =  !1»  inches- 
n'c  =  "^if  =  68  slots; 

One-half  of  the  winding  space  being  occupied  by  each  winding, 
34  slots  of  24  wires  constitute  one  winding.     The  secondary 


§150]  EXAMPLE    OF  MOTOR   GENERATOR.  657 

winding  requiring  four  times  the  area,  4  No.  16  wires  in 
multiple  form  one  secondary  conductor.  Making  the  primary 
commutator  of  68,  and  the  secondary  of  34  divisions,  the 
primary,  or  motor  winding  consists  of  68  coils  of  12  turns  of 
1  No.  16  B.  W.  G. ;  and  the  secondary,  or  generator  winding, 
of  34  coils  of  6  turns  of  4  No.  16  B.  W.  G.  wires.  Hence  the 
length  of  the  armature  core: 

/>  =  444X.2 
34  X  24 

=  2  240  ^  webers. 
34  X  24     x   145° 

2,240,000  rt    . 

b&  =  -  -  —  24-  inches. 

2  x  85,000  X  6£  x  .90 

The  length,  weight,  and  resistance  of  the  primary  winding  are, 
respectively: 

,r  x  34  X  *4  =  ,355  feet. 


12 

wt&l  =  .00000303  X  4225  X  1355  =  17$lbs. 

7-a,  =  -  X  1355  X  .00245  ='.83  ohm,  at  15.5°  C. 
4 

The  length  of  the  secondary  winding  is  one-quarter  that  of 
the  primary,  the  weight  is  precisely  the  same,  and  the  resist- 
ance is  —3  times  that  of  the  primary,  or 

raa  =  '—i  =  .052  ohm,  at  15.5°  C. 

c.   Dimensioning  of  Magnet  Frame. — (Fig.  375.) 

&  =  1.34  X  2,240,000  =  3,000,000  webers. 

3,000,000 
*->m  =  ~       o        -  =  17.7  square  inches. 

2    X   05,000 

Cylindrical  cores  being  selected  their  diameter  is: 
<4i  =  \f   17-7  X  -  =  4f  inches. 


658  DYNAMO-ELECTRIC  MACHINES. 

Length  of  cores: 
Width  of  yoke : 
Thickness  of  yoke : 

T  *T       *T 

=  2}  inches. 
"^ 

Bore  of  field: 


[§150 


4.  —  6J-  inches. 
6 1  inches. 

17-7 


—  i  if  +  2  X  TV  =  11 J  inches. 


Fig.  375. — Dimensions  of  Armature  Core  and  Magnet  Frame, 
5^  KW.     Double  Horseshoe  Type  Motor-Generator. 

Chord  of  polar  embrace : 

/ip  =  n£  x  sin  63°  =  10}-  inches. 

Total  width  of  polepieces: 

/z'p  =  ioj  -+-  2  X  %  =  11 J  inches. 

Distance  between  pole-corners: 

/'p  ==  n^  x  sin  27°  =  5J  inches. 
d.    Calculation  of  Magnetizing  Forces.  — 

Ze  =  36  x  24  x   —   X  .88  =  412  feet. 


§  15O]  EXAMPLE   OF  MOTOR   GENERATOR.  659 

By  (144),  P-   205: 

468  X    io8 

3C    =  -  .   «  =  23,400  lines  per  square  men. 

72   x  412  X  67-1 

OC"  X  s>c  =  23,400  X  674  =  1,580,000. 
Ratio  of  radial  clearance  to  pitch: 


.. 
2  X  H 

Factor  of  field-deflection,  by  Table  LXVIL,  p.  230:  £13  =  4.5. 
„-.  atg  =  .3133  X  23,400  X  4-5  X  (n£  —  nf) 
=  4120  ampere-turns. 

By  (237),  P-  343^ 

l\  =  7f  x  n  x  9°  ~^Q27  4-  2j  +  2  x  H  =  i  if  inches. 

/«»*.)  ==  ^r  [/  feooo)  4-7(42,500)]  =  ^_±j 

=  23.9  ampere  -turns  per  inch. 
.  •  .  at&  =  23.9  x  i  if  =  280  ampere-turns. 

l"m  —  44  inches,  length  of  circuit  in  frame. 
/  ((B"a)  ~  7(85,000)  =  44  ampere-turns  per  inch  (cast  steel). 
.  •  .  (jfm  —  44  x  44  =  1940  ampere-turns. 

AT  —  4120  -j-  280  -j-  1940  =  6340  ampere-turns. 

e.    Calculation  of  Magnet  Winding.  — 

flm  =  25°  C.     rx  =  45#- 
Depth  of  winding  space: 
hm  =  1  inch. 

^T  =  (4|  +  i)  X  TT  =  18  inches. 
^  =  6|  x  TT  x  2  x  (6J  —  J)  =  255  square  inches. 

Connecting  all  four  cores  in  series  across  the  primary 
terminals,  each  circuit  of  two  cores  will  take  one-half  the 
voltage,  or  250  volts,  hence: 

6740         18 

A"h  =    250     X  7i  X  I>45  X  (l  +  -°°4  X  25<>) 
=  60,5  feet  per  ohm, 

which  corresponds  to  No.  23  B.  W.  G.  (.025"  -f  .005"). 


660  DYNAMO-ELECTRIC  MACHINES.  [§  150 


P'sh  =     ~    X  255  x  1-45  =  I23  watts. 
7° 

N^  —  634°    (  25°   =  12,800  turns,  per  magnetic  circuit,   or 

6400  turns  per  core. 
Each  layer  can  hold 


=  200  wires. 


.030 
Number  of  layers  required  : 

6400  ^o 

200 
Actual  winding  depth: 

^'m  =  32 .  X  .030  =  .96  inch. 

Zsh  =  4  x  200  X  32  X  --  =  38,400  feet,  total,  4  cores. 
rsh  =  -~-         =  634  ohms,  at  15.5°  C. 

r'sh  =  634  X  (i  +  .004  x  25)  =  697  ohms,  at  40.5°  C. 
r"Sh  =  697  X  1.45  =  1010  ohms,  entire  shunt-circuit. 

/Sh  —  ~ —  =  .495  ampere. 
1010 

Actual  excitation,  full  load: 

AT  —  2  x  200  x  32  X  .495  =  6340  ampere-turns. 
Weight  of  magnet  winding: 

«//sh  —  38,400  x  .00189  =  72J  pounds,  total,  bare  wire: 

o//'Bh  =  1.07  x  72^  =   78  pounds,  total,  covered  wire,    or 
19J  pounds,  covered,  of  No.  23  B.  W.  G.  wire  per  core. 


INDEX. 

(Numbers  indicate  pages.} 


Absolute  units,  7,  47,  199,  332,  333 
Accessibility  of  parts  in  dynamos, 

287,  432 
Accumulator  charging   dynamos, 

91,  92,  461,  462 
Act  of  commutation,  29 
Active  wire  in  armature,  49,  55 
Activity,  electrical,  in   armature, 
405,  407,  420,  422,  628,  637,  644 
Addenbrooke,     on    insulation-re- 
sistance of  wood,  85 
Addition  of  E.  M.  Fs.  in  closed 

coil,  12 

Adjustment  of  brushes,  29 
Advantages  of  combination  mag- 
net-frames, 294 

—  of  drum-wound    ring    arma- 
tures, 35 

—  of  iron  clad  types,  286 

—  of    multipolar   dynamos,    33, 
34,  285 

—  of  open  coil  armatures,  144 

—  of  oxide  coating  of  armature 
laminae,  93 

—  of    stranded    armature    con- 
ductor, 528,  553 

—  of    toothed    and    perforated 
armatures,  61,  62,  63 

—  of  unipolar  dynamos,  25,  26 
Air-ducts  in  armature,  94,  590 
Air-friction,  407,  526 

Air-gaps,  ampere-turns    required 
for,  339,  340 

—  graduation  of,  295 

—  influence  of  change  of,  483,  484 

—  length   of,  62,  208,  433,    469, 
470-472,  483 

—  permeance  of,  217,  224-231 
Alignment  of  bearings,  304,  409 
Allowance  for  armature-binding, 

75,  507,  536 

—  for  clearance,   209,  210,    518, 
536,  543,  558,  576,  583,  604 

—  for  flanges  on  magnet-cores, 
523,  542,  576,  595,  650 


Allowance  for  height  of  commu- 
tator-lugs, 514 

—  for  spaces  between  armature- 
coils,  73,  506,  638 

—  for  spread  of  magnetic  field, 

529 

—  for  stranding    of    armature- 
conductor,  530 

Alternating    current,    production 
of,  12 

—  rectification  of,  13 
Alternators,  unipolar,  24 
Aluminum,  in  cast  iron,  in,  293, 

312,   313,   314,   315,   316,    336, 

337,  338 

Aluminum-bronze,  189 
"  American  Giant  "  dynamo,  272, 

281 
Amperage,    permissible,    56,    57, 

132,  133,  183 
Ampere-turn,  the  unit  of  exciting 

power,  333 
Ampere-turns,  calculation  of,  339- 

356,    520,    537,    547,    560,    575, 

585,  605,  638,  645,  657 
Analogy  between  magnetic  and 

electric  circuit,  354 
Angle  of  belt-contact,  193 

—  of  lag,  30,  421 

—  of  lead,  30,  349,  350,  421 

—  of  pole-space,  210,  211 
Application    of    connecting    for- 
mula, 152-155 

—  of     generator     formulae     to 
motor  calculation,  419 

—  of  permeance  formula,   220- 
223 

Arc  of  belt-contact,  193 

—  of  polar  embrace,  49 
Arc-lighting  dynamos,  designing 

of,  455-459 

—  magnetic  density  in  armature 
of,  91 

—  regulation  of,  458,  459 

—  series-excitation  of,  37 
Area,    see    Sectional    Area,    and 

Surface. 


661 


662 


INDEX. 


Armature,  calculation  of,  45-195, 
413-416,  505,  527,  552,  566,  580, 
587,  603,  629,  638,  644,  652,  656 

—  circumflux  of,  131 

—  closed  coil-  and  open-  coil,  143 

—  cylinder-,  or  drum-,  see  Drum- 
Armature. 

—  definition  of,  4 

—  disc-,  see  Disc-Armature. 

—  energy-losses  in,  107-122 

—  load  limit  and  maximum  safe 
capacity  of,  132-135 

—  perforated,    or    pierced,   see 
Perforated  Armature. 

—  pole-,    or     star-,     see     Star- 
Armature. 

—  principles  of  current-genera- 
tion in,  3 

—  ring-,  see  Ring-Armature. 

—  running-value  of,  135,  136 

—  smooth     core-,     see    Smooth 
Core  Armature. 

—  toothed    core-,  see    Toothed 
Core  Armature. 

Armature-calculation,  formulae 
for,  45-195 

—  practical    examples   of,    505, 
527,    552,    566,    580,    587,   603, 
629,  638,  644,  652,  656 

—  simplified  method  of,  413-416 
Armature-coils,  formula  for  con- 
necting of,  152-155 

—  grouping  of,  147-151 
Armature-conductor,   active    and 

effective,  49 

—  length  of,  55,  94 

—  size  of,  56 
Armature-conductors,  number  of, 

76,  77 

—  peripheral  force  of,  138-140 
Armature-core,  diameter  of,  58 

—  insulation  of,  78-82 

—  length  of,  72,  76 

—  magnetic  density  in,  90,  91 

—  magnetizing  force  for,  340-343 

—  radial  depth  of,  92 
Armature-current,  total,  in  shunt 

and  compound  dynamos,  109 

—  volume  of,  131 

Armature-divisions,  number  of,  90 
Armature-induction,  specific,  51 

—  unit,  47-50 
Armature-insulations,  selection  of 

material  for,  83-86 

—  thickness  of,  82 
Armature-reaction,  compounding 

motor  by,  649 

—  magnetizing  force  for   com- 
pensating, 348-352 


Armature-reaction,  prevention  of, 
463-470 

—  regulating  for  constant  cur- 
rent by,  456 

Armature-thrust,  140-142,  513,  534 
Armature-torque,  63,  137,  138,  513, 

534 

Armature-winding,  arrangement 
of,  87,  507,  529,  554,  58i,  589, 
604,  657 

—  circumferential    current-den- 
sity in,  130-132 

—  connecting-formula  for,   152- 

155 

—  energy  dissipated  in,  108 

—  fundamental  calculations  for, 

47 

—  grouping  of,  147-151 

—  mechanical  effects  of,  137-142 

—  qualification    of    number    of 
conductors  for,  155-167 

—  rise-  of  temperature  in,  126- 

130 
-  types  of,  143-147 

—  weight  of,  101,  102 

Arnold,  Professor  E.,  on  arma- 
ture-winding, 152 

—  on  unipolar  dynamos,  25 
Arrangement  of    armature-wind- 
ing, 87,  507,  529,  554,  581,  589, 
604,  657 

—  of    field-poles    around    ring- 
armature,  98 

—  of  magnet-winding  on  cores, 
387,   401,    551,    564,    576,    599, 
613,  635,  641,  655,  660 

Asbestos,  for  armature-insulation, 

78,  79,  85,  93,  94 
"  Atlantic  "  fan-motor,  282 
Attracting  force  of  magnetic  field, 

140,  141 

Auxiliary  pole  method,  469 
Available    height    of    armature- 
winding,  74 

—  of  magnet-winding,  377 
Average    efficiencies    of    electric 

motors,  422 

—  E.  M.  F.,  8,  9,  19,  20,  21 

—  magnet  density  in  armature- 
core,  III,  I2O 

—  pitch    of    armature-winding, 
158-167 

—  relative  permeance  between 
magnet-cores,  231,  238 

—  traction-resistance,  440 

—  turn,  length  of,  on  magnets, 

374 

—  useful  flux  of  dynamos,  212- 
214 


INDEX. 


663 


Average  values  of  hysteretic  re- 
sistance, no 
—  volts    between     commutator 

sections,  88,  151 
—  weight  and  cost  of  dynamos, 

412 
Axial  multipolar  type,  270,  282 


B 


Back  E.  M.  F.,  see  Counter  E. 
M.  F. 

—  pitch    of    armature-winding, 
159-167 

Backward  lead,  see  Angle  of  Lag. 

Bacon,  George  W.,  on  magnetism 
of  iron,  335 

Bar  armatures,  101,  567,  569,  588 

Base,  or  bedplate,  of  dynamo,  299, 
300 

Battery-motors,  54,  91,  92 

Baumgardt,  L.,  on  dimensioning 
of  toothed  armatures,  67 

Baxter,  William,  on  seat  of  elec- 
tro-dynamic force  in  iron  clad 
armatures,  64 

Bearings,  184,  186,  187,  190,  191, 
192,  303-305,  5i6 

Belt-velocity,  193 

Belt-driven  dynamos,  see  High- 
Speed  Dynamos. 

Belts,  calculation  of,  193-195,  517 

—  losses  in,  409 

Bifurcation   of  current  in   arma- 
ture, 48,  49,  51,  104 

Binding-posts,      see      Conveying 

Parts. 

Binding  wires,  for  armatures,  75 
Bipolar  dynamos,  act  of  commuta- 
tion in,  29 

—  classification  of,  269,  270-278, 
286 

—  connecting  formula  for,  153 

—  field-densities  for,  54 

—  generation  of  current  in,  27 

—  running  value  of,  136 
Bipolar  iron   clad  type,  234,  235, 

247.  255,  263,  637' 

Bipolar  types,  comparison  of,  249- 
256 

—  practical  forms  of,  270-278 
Blank  poles,  469 

Bobbin,  formulae  for  winding  of, 
•       359-363 

Bolted  contact,  182,  183 
Booster,  see  Motor-Generator. 
Bore  of  polepieces,  209,  210 
Bottom-insulation  of  commutator, 
171 


Brass,  current-densities  for,  183 

—  for  brushes.  173,  176 

—  for  commutators,  169 

—  for  dynamo-base,  300 

—  safe  working  load  of,  189 
Breadth  of  armature  cross-section , 

92 

—  of  armature-spokes,  189,  190, 
5i6 

—  of  belt  and  pulley,  193-195 ,517 

—  of  brush-contact,  175,  514 
Breslauer,  Dr.  Max,  on  hysteresis- 
loss  in  toothed  armatures,  591 

Bristol-board,  for  armature-insu- 
lation, 85 
Brunswick,  on  change  of  air-gaps, 

483 

Brushes,  arrangement  of,  on 
commutator,  169,  170,  174 

—  best  tension  for,  176-180,  515 

—  dimensioning  of,  175,  176,  515 

—  displacement  of,  30 

—  material  and  kinds  of,  171-174 
—  number    of,    for    multipolar 

dynamos,  34 

Brush-holders,  181 

Buck,  H.  W.,  on  commutator- 
brushes,  177 

Burke,  James,  on  insulating  ma- 
terials, 86 

Bushing,  pole-,  Dobrowolsky's,  49 

Butt-jointing  of  magnet-frame, 
306,  307 


Cables,  see  Stranded  Wire  Con- 
ductors. 

Calculation  of  armature,  45-195, 
413-416,  505,  527,  552,  566,  580, 
587,  603,  629,  638,  644,  652,  656 

—  of  efficiencies,   405-410,    526, 
546,  565,  578,  602,  636,  643 

—  of    electric   motors,   419-442, 
628-652 

—  of  field  magnet  frame,  313- 
327,    5i7»    534.    557.    572,    583, 
593,  607,  632,  639,  646,  657 

—  of  generators  for  special  pur- 
poses, 455-463 

—  of  leakage-factor,  217-263,  519, 
536,    559,    573,    584,     595,  609, 
614-628,  633 

—  of    magnetic    flux,    200-216, 
517,    53i,    554,    568,    581,    589, 
605,  638,  645,  657 

—  of  magnetizing  forces,  339-3 56, 
520,    537,    547,    560,    575,    585, 
596,  610,  634,  640,  647,  654,  658 


664 


INDEX. 


Calculation  of  magnet-  win  ding, 
359-401,  486-497,  522,  540,  549, 
562,  576,  599,  612,  635,  640,  649, 
654,  659 

—  of  motor  generators,  452-454, 

655 

—  of    railway  motors,   431-442, 


—  of  unipolar  dynamos,  443-451, 
652 

Canfield,    M.    C.,    on    disruptive 

strength  of  insulating  mate- 

rials, 86 
Canvas,   for  armature-insulation, 

78,  79 
Capacity,  maximum  safe,  of  arma- 

ture, 132-135 

—  of  railway  motor  equipment, 
440-442 

Carbon-brushes,  171-180,  183 
Card-board  (press-board)  for  arma- 

ture-insulation, 78,  79,  80,  85 
Cast  iron,  in,  178,  189,  288,  312, 

313,  448 

—  steel,  in,  189,  288,  289,  293, 
448 

Cast-  wrought     iron,     see     Mitis 

Metal. 

Causes  of  sparking,  see  Sparking. 
C.-G.-S.  units,  7,  47,  199,  332,  333 
Characteristic  curves,  476-483 
Charging  accumulators,  dynamos 

for,   see  Accumulator-Charg- 

ing Dynamos. 
Checks  on  armature  calculation, 

130,  132,  135 
Cheese-cloth,  varnished,  for  arma- 

ture-insulation, 85 
Chord-winding,  see   Ring  Arma- 

ture, Drum-  Wound. 
Circuit,  closed  electric,  6,  317 

—  magnetic,  317,  331 
Circumflux  of  armature,  131 
Clamped  contact,  182,  183 
Classification  of  armatures,  4 

—  of    armature-windings,    143, 
144 

—  of  dynamos,  35,  269,  270 

—  of  field-magnet  frames,  269, 
270 

—  of  inductions,  23 
Clearance  between  armature  and 

pole-face,  209,  210 

—  between    pole-corners,     207, 
208 

Closed  coil  winding,  143,  144,  458 
Coefficient,  see  Factor. 
Coil,  closed,  moving  in  magnetic 
field,  n,  12 


Coils,  number  of,  in  armature,  87- 
89 

—  short-circuited,  in  armature, 
28,  30,  149,  174,  175,  298 

Coil- winding  calculation,  359-373 
Collection  of  current,  by  means  of 
collector  rings,  12 

—  by  means  of  commutator,  13 

—  energy-loss  in,  176-180 

—  sparkless,  see  Sparking. 
Collection  of  large  currents,  174 
Collector,  see  Commutator. 
Combination  brushes,  173,  174 
Combination-frames,    advantages 

of,  294 

—  calculation    of    flux  in,    260 r 
261,  621 

—  joints  in,  306-309 
Combination-method  of  speed  con- 
trol for  railway  motors,  436 

Combination  of  shunt-coils  for 
series  field  regulation,  378- 
382,  523-526 

Commercial  efficiency,  see  Effi- 
ciency, Commercial. 

—  copper,  specific  resistance  of, 
104,  105 

—  wrought    iron,    permeability 
of,  311 

Commutation,  act  of,  29 

—  effect    of,   in  generator  and 

motor,  30 

—  sparkless,  promotion  of,   30, 
62,  172,  173,  297,  298,  299,  459,. 
463-470,  471,  472 

—  sparkless,  in  toothed  and  per- 
forated armatures,  62 

Commutator,  construction  and  di- 
mensioning of,  168-170,  514 

—  distribution   of  potential   on, 

3I~33  •   1      f 

—  principle  of,  13,14 

—  thickness  of  insulation  for,  171 
Commutator-divisions,    difference 

of  potential  between,  88, 151 

—  number  of,  87,  88 
Compactness  of  railway  motors r 

432 

Comparison  of  efficiency-curves  of 
motors,  431 

—  of  various  types  of  dynamos, 
248-256 

Compensating  ampere-turns,  see 
Armature-Reaction. 

Compound-dynamo,  constant  po- 
tential of,  43 

—  efficiency  of,  42,  43,  406,  408 

—  E.  M.  F.  allowed  for  internal 
resistance  of ,  56 


INDEX. 


665 


Compound-dynamo,  fundamental 
equations  of,  41,  42,  43 

—  over-compounding  of,  43,  396 

—  total  armature  current  in,  109 
Compound-motor,    406,    408,   426, 

428,  644 

Compound-winding,  calculation 
of,  395-401,  456,  549,  563,  599, 
649 

—  principle  of,  41-43 
Conductivity,  electrical,  of  copper 

and  iron,  119 

Conductor,  armature-,  see  Arma- 
ture-Conductor. 

—  describing  circle  in  magnetic 
field,  8 

—  motion  of,  in  uniform  mag- 
netic field,  5 

Conductor- velocities,  52 

Connecting-formula  for  armature- 
winding,  152-155 

Consequent  poles,  275,  286,  327, 
603 

Constant  current  dynamos,  see 
Arc-Lighting  dynamos. 

—  excitation   in   compound  dy- 
namo, 43 

—  potential  dynamos,  43 

—  power  work,  motors  for,  429, 
431,  628 

—  speed  motors.  63,  426,  427 
Construction-rules  for  field-frame, 

288-309 

Contact-area  of  commutator- 
brushes,  169,  174-176 

Contact-resistance  of  commutator-, 
brushes,  177-180 

Contacts,  various  forms  of,  181- 
183 

Continuous  current,  production  of, 
13,  14,  22 

Conversion,  efficiency  of,  see  Effi- 
ciency, Gross. 

—  of  motor  into  generator,  419, 
628,  637,  644 

Conveying  parts,  181-183 
Cooling    surface,    see    Radiating 

Surface. 
Copper,  current-densities  for,  183 

—  physical    properties   of,    101, 
104,  113,  362 

Core,  see  Armature-Core  or  Mag- 
net-Core, respectively. 

Corsepius,  on  magnetic  leakage, 
262 

Cost  of  dynamos,  288,  289,  300,  411, 
412 

Cotton,  for  armature-insulation, 
78,  85 


Cotton  covering  on  wires,  insulate 
ing  properties  of,  85 

—  weight  of,  103,  367 
Counter     Electro-Motive     Force, 

421,  423,  434,  438,  453,  461 

—  Magneto-Motive    Force,    see 
Armature-Reaction. 

Cox,     E.     V.,    on     Commutator- 
brushes,  177 
Critical     brush-tension,     176-179, 

5i5 

Crocker,  Professor  F.  B.,  on  high- 
potential  dynamos,  462 

—  on  unipolar  dynamos,  25,  26 
Cross-connection  of  commutator- 
bars,  35,  155 

Cross-Induction,  see  Armature  Re- 
action. 

Cross-Magnetization,  see  Arma- 
ture Reaction. 

Cross-Section,  see  Sectional  Area. 

Crowding  of  magnetic  lines  in 
polepieces,  295 

Current,  alternating,  see  Alterna- 
ting Current. 

—  collection  of,  from  armature 
coil,  12 

—  commutated,   fluctuations  of, 
14-21 

—  constant,    see   Constant  Cur- 
rent. 

—  continuous,     direct,    or    uni- 
directed,  see  Continuous  Cur- 
rent. 

—  direction  of,  in  closed  coil,  12 

—  in  single  inductor,  TO 

—  in  electric  motors,  427-429, 642 
Current-density,   circumferential, 

of  armature,  130-132 

—  in  armature-conductor,  56,  57 

—  in  magnet-core,  364,  365 

—  permissible,  in  materials,  183 
Currents,  eddy,  or  Foucault,  see 

Eddy  Currents. 

Curve  of  average  E.  M.  F.  in- 
duced in  armature,  19 

—  of  E.  M.  Fs.,  rectified,  14 

—  of  induced  current,  13 

—  of  induced  E.  M.  F.,  13 
Curves,  characteristic,  476-483 

—  of  contact-resistance  and  fric- 
tion  of    commutator-brushes, 
177,  178 

—  of  eddy  current  factors,  121 

—  of  hysteresis  factors,  1 14 

—  of  potentials    around  arma- 
ture, 32,  33 

—  of  relative  hysteresis-heat  in 
armature-teeth,  68 


666 


INDEX, 


Curves    of    specific   temperature- 
increase  in  armature,  128 
—  of    temperature-effect    upon 
hysteresis,  117 

Cutting  of  magnetic  lines,  3,  5,  6, 
8,  9,  12,  22,  27,  47,  48,  52,  200, 
201 

Cycle  of  magnetization,  109,  no, 
in,  113,  115,  119,  121 

Cylinder  armature,  see  Drum  Ar- 
mature. 

Cylindrical  magnets,  232,  234, 289, 
2*91,  318,  319,  320,323,  369,  374, 
375 


Data  for  winding  armatures,  155- 
167 

—  general,    of  railway  motors, 

435 

Dead  wire  on  armature,  94 
Deflection  of  lines  of  force  in  gap- 
space,  see  Distortion  of  Mag- 
netic Field. 
Definition  of  armature,  4 

—  of  closed  and  open  coil  wind- 
ing, 143 

—  of  dynamo-electric  machine, 

—  of  generator,  3 

—  of  magnetic  units,  199 

—  of  motor,  3 

—  of  unipolar,  bipolar,  and  mul- 
tipolar  induction,  23 

—  of  unit  induction,  47 
Demagnetizing    action    of    arma- 
ture, see  Armature-Reaction. 

Density  of  current,    56,    57,    132, 
133.  183 

—  of  magnetic  lines,  54,  91,  313 
Depth  of  armature-core,  92,  341, 

342 

—  of  armature-winding,  70,  71, 
74,  75 

—  of  magnet-winding,  317,  361, 
.371,  375,  377.  386,  387 

Design  of  current  conveying  parts, 
181-183 

—  of  generators  for  special  pur- 
poses, 45  5-463 

—  of  magnet-frames,  270-309 

—  of  motors  for  different  pur- 
poses, 429,  430 

—  of  railway  motors,  432 
Developed  winding  diagrams,  146, 

147 

Diagram  of  closed  coil  armature- 
winding,  144 


Diagram     of    doubly    re-entrant 
winding,  150 

—  of  duplex  winding,  149 

—  of    drum-wound    ring   arma- 
ture, 101 

—  of  lap-winding,  145,  146 

—  of    long    shunt     compound- 
wound  dynamo,  42 

—  of  mixed  winding,  147 

—  of  open  coil  armature  wind- 
ing, 144 

—  of  ordinary  compound-wound 
dynamo,  41 

—  of  parallel  armature  winding, 
165,  166 

— -  of  series  armature  winding, 
157 

—  of  series  winding  with  shunt- 
coil  regulation,  378 

—  of  series-wound  dynamo,  36 

—  of  shunt-wound  dynamo,  38 

—  of  simplex  winding,  149 

—  of  singly  re-entrant  winding, 
150 

—  of  spiral  winding,  145 

—  of  wave  winding,  146,  147 
Diamagnetic   materials,    permea- 
bility of,  311 

Diameter  of  armature-core,  58,  60, 
61 

—  of  armature-shaft,  184-187,516 

—  of  armature-wire,  57 

—  of  commutator  brush-surface, 
168,  514 

—  of  heads  in  drum  armatures, 
124 

'  — of  magnet  wire,  361,  362,  365 

—  of  pulley,  191,  517 
D.ielectrics,  properties  of,  83-86 
Difference  of  potential,  see  Elec- 
tro-Motive Force. 

Differentially  wound  motor,  406, 

408,  426,  428,  644 
Dimensions  of  armature-bearings, 

184,  191,  516 

—  of  armature-core,  58-86 

—  of  belts,  194,  517 

—  of    driving-spokes,     188-190, 
5i6 

—  of  magnet-cores,  319-324 

—  of  toothed  and  perforated  ar- 
matures, 65-72 

—  of    unipolar    dynamos,    443- 
446,  652 

—  see    also    Length,     Breadth, 
Diameter,      Sectional     Area, 
etc. 

Direct-driven  machines,  see  Low- 
Speed  Dynamos. 


INDEX. 


667 


Direction  of  current,  10,  30 

—  of  E.  M.  F.,  9 

—  of  rotation,  10,  12,  422 
Disadvantages  of  laminated  pole- 
pieces,  292 

—  of  multiple  magnetic  circuits, 
286,  290 

—  of  multipolar  frames  for  small 
dynamos,  285 

—  of  paper-insulation  between 
armature-laminae,  93 

—  of  toothed  and  perforated  ar- 
matures, 61,  62 

Disc-armature,  definition  of,  4 
Disruptive  strength  of  insulating 

materials,  83,  84,  85 
Dissipation  of  energy  in  armature 

core,  i 10-122 

—  in  armature  winding,  108,  109 

—  in  magnet  winding,  370,  372 
Distance    between   magnet-cores, 

320-324 

—  between  pole-corners,  207,  208 
Distortion  of  magnetic  field,  225, 

230,  349, 456 
Distribution    of   flux  in   dynamo, 

397-399 

—  of  potential  around  armature, 

.    3i,  33 
Division-strips  in  drum  armatures, 

Dobrowolsky's  pole-bushing,  49, 
296 

Double  horseshoe  type,  classifica- 
tion of,  269,  276 

—  magnetic  leakage  in,  242,  252, 
253,  263 

Double   magnet   multipolar  type, 

270,  283 
Double  magnet  type,  classification 

of,  269,  275,  276 

—  leakage  factor   of,    252,   254, 
263 

—  permeance  across  polepieces, 
in,  240,  242 

—  permeance  between  magnet 
cores  in,  237,  238 

—  permeance      between      pole- 
pieces  and  yoke  in,  246,  247 

Doubly  re-entrant  armature-wind- 
ing, 150,  156,  160,  161 

Drag,  magnetic,  see  Force,  Elec- 
tro-Dynamic. 

Draw-bar  pull  of  railway  motors, 
440-442 

Driving-horns  for  drum  armatures, 
.  73.  HO 

Driving-power  for  generator,  408, 
420 


Driving-spokes  for  ring  armatures, 

186,  188-190,  516 
Drop  of  voltage  due  to  internal 

resistances,  37,  39,  43 
Drum  armatures,   allowance    for 

division-strips  in,  60 

—  bearings  for,  191 

—  core-densities  for,  91 

—  definition  of,  4 

—  diameters  of  shafts  for,  186 

—  heating  of,  129,  130 

—  height  of  winding  space  in, 

—  insulation  of,  78,  79 

—  radiating  surface  of,  123-125 

—  size  of  heads  in,  123,  124 

—  speeds  and  diameters  of,  60 

—  total  length  of  conductor  on, 

95 

Duplex,  or  double,  armature  wind- 
ing, 149,  150,  151,  156,  160,  161, 
165,  166,  167 

Dynamo-electric  machines,  defini- 
tion of,  3 

—  physical  principles  of,  3 
Dynamo-graphics,  476-502 
Dynamos,   bipolar,    see      Bipolar 

Dynamos. 

—  constant   current,    see    Arc- 
Lighting  Dynamos. 

—  Electro-plating,    Electro-typ- 
ing, etc.,  see    Electro-Metal- 
lurgical Dynamos. 

—  for    charging    accumulators, 
see    Accumulator     Charging 
Dynamos. 

—  list  of,  considered  in  prepara- 
tion of  Tables,  see  Preface. 

—  multipolar,     see     Multipolar 
Dynamos. 

—  unipolar,    or  homopolar,  see 
Unipolar  Dynamos. 

Dynamos  of  various  Manufactur- 
ers: 

Aachen  Electrical  Works,  277 

Actien-Gesellschaft  Elektrici- 
tatswerke,  273,  274,  278,  281 

Adams,  A.  D.,  see  Commercial 
Electric  Co. 

Adams  Electric  Co.,  270 

Akron  Electric  Manufacturing 
Co.,  275 

Alioth,  R.,  &  Co.,  281 

Allgemeine  Electric  Co.,  49,  281 

Alsacian  Electric  Construction 
Co.,  281 

Atkinson,  see  Goolden  &  Trpt- 
ter. 

Aurora  Electric  Co.,  272 


668 


INDEX. 


Dynamos  of  various  Manufactu- 
rers— Con  tin  ued. 
Bain,  Force,  see  Great  Western 

Electric  Co. 

Baxter    Electrical    Manufactur- 
ing Co.,  276,  281 
Belknap  Motor  Co.,  272,  280 
Berliner  Maschinenbau  Actien- 

Gesellschaft,  273,  281 
Bernard  Co.,  271 
Bernstein  Electric  Co. ,  274 
Boston  Fan  Motor  Co.,  274 
Brown,  C.  E.  L.,  see  Oerlikon 

Machine  Works. 
Brush    Electrical    Engineering 

Co.,  278,  282,  283 
Brush  Electric  Co.,  276,  459 
11  C.  &  C."  (Curtis  &   Crocker) 
Electric  Co.,  270,  276,  282,  283 
Card  Electric   Motor  and    Dy- 
namo Co.,  272,  274,  278 
Chicago  Electric  Motor  Co.,  274 
Clarke,  Muirhead  &  Co.,  272 
Claus  Electric  Co.,  280 
Columbia  Electric  Co.,  271,  280 
Commercial  Electric  Co.  ,275 
Crocker- Wheeler  Electric    Co., 

272,  280,  398 

Crompton  &  Co.,  276,  277 
Cuenot,  Sauter  &  Co.,  282 
Dahl  Electric  Motor  Co.,  281 
"  D.  &  D."  Electric  Co.,  274 
De  Mott  Motor  and  Battery  Co., 

275 

Desrozier,  M.  E.,  282 
Detroit  Electrical  Works,    271, 

277 

Detroit  Motor  Co.,  272 
Deutsche       Elektricitatswerke, 

278,  281 
Dobrowolsky,  M.  von   Dolivo-, 

see  Allgemeine  Electric  Co 
Donaldson-Macrae  Electric  Co., 

273 

Duplex  Electric  Co.,  275,  285 
Eddy    Electric     Manufacturing 

Co.,  280 
Edison    General    Electric    Co., 

168,  270,  284,  305,  398,  435,  458, 

621 
Edison  Manufacturing  Co.,   275, 

278 

Eickemeyer  Co.,  277 
Elbridge   Electric    Manufactur- 
ing Co.,  274 

Electrical  Piano  Co.,  275 
Electro-Chemical  and  Specialty 

Co.,  282 
Electro-Dynamic  Co.,  276 


Dynamos  of  various  Manufactu- 
rers— Continued. 
Electron     Manufacturing     Co., 

170,  271,  274,  284 
Elektricitats-A  c  t  i  e  n-G  e  s  e  1 1- 

schaft,  281 

Elliot-Lincoln  Electric  Co.,  284 
Elphinstone  &  Vincent,  284 
El  well-Parker  Electric  Construc- 
tion Corporation,  277,  284 
Erie  Machinery  Supply  Co.,  278 
Esson,  W.  B.,  see  Patterson  & 

Cooper. 

Esslinger  Works,  283 
Excelsior  Electric  Co.,  272,  273, 

459 

Fein  &  Co.,  275,  276,  277,  281 
Fontaine  Crossing  and  Electric 

Co.,  276 
Ford-Washburn  Storelectric  Co. , 

276 

Fort  Wayne   Electric   Corpora- 
tion, 170,  274,  277,  280,  283,  458 
Fritsche  &  Pischon,  282 
Fuller,    see    Fontaine  Crossing 

and  Electric  Co. 
Garbe,    Lahmeyer    &  Co.,   see 

Deutsche   Elektricitatswerke. 
Ganz  &  Co.,  273,  281 
General  Electric  Co.,  170,  270, 

277,  278,  280,  282,  284,  435 
General  Electric  Traction  Co., 

Goolden  &  Trotter,  274 

Granite  State  Electric  Co.,  277 

Great  Western  Electric  Manu- 
facturing Co.,  273,  280,  458 

Greenwood  &  Batley,  274 

Giilcher  Co.,  170 

Helios  Electric  Co.,  276,  282 

Henrion,  Fabius,  282. 

Hochhausen,  see  Excelsior  Elec- 
tric Co. 

Holtzer-Cabot  Electric  Co. ,  272, 
274 

Hopkinson,  Dr.  J.,  see  Mather 
and  Platt. 

Immisch  &  Co.,  276,  618 

India  Rubber,  Guttapercha  and 
Telegraph  Works  Co. ,  272 

Interior  Conduit  and  Insulation 
Co.,  277,  283 

Jenney  Electric  Co.,  273 

Jenney  Electric  Motor  Co.,  274 

Johnson  &  Phillips,  273 

Johnson  Electric  Service  Co., 
278 

Kapp,  Gisbert,  see  Johnson  & 
Phillips. 


INDEX. 


669 


Dynamos  of  various  Manufactu- 
rers— Con  tin  ued. 
Kennedy,    Rankine,  see  Wood- 
side  Electric  Works. 
Keystone  Electric  Co.,  272,  275 
Knapp    Electric    and     Novelty 

Co.,  272 

Kummer,  O.  L.  &  Co.,  see  Ac- 
tien-Gesellschaft  Elektricitats- 
werke. 

Lahmeyer,  W.,  see  Aachen  Elec- 
trical Works. 
Lahmeyer,  W.  &  Co.,  see  Elek- 

tricitats-Actien-Gesellschaft. 
Lafayette  Engineering  and  Elec- 
tric Works,  278 
La  Roche  Electrical  Works,  272, 

277 

Lawrence,  Paris  &  Scott,  276 
Lundell,    Robert,    see    Interior 

Conduit  and  Insulation  Co. 
Mather  &  Platt,  272,  276 
Mather  Electric  Co.,   275,   280, 

281 

Mordey,  W.  H.,  see  Brush  Elec- 
trical Engineering  Co. 
Muncie  Electrical  Works,  278 
Naglo  Brothers,  274,  275,  276,  281 
National   Electric    Manufactur- 
ing Co.,  272 

Novelty  Electric  Co.,  271 
Oerlikon  Machine    Works,  276, 

278,  281,  435 

Onondaga  Dynamo  Co.,  277 
Packard  Electric  Co.,  274 
Patterson  &  Cooper,  170,  273,  614 
Ferret,  see   Electron  Manufac- 
turing Co. 

Porter  Standard  Motor  Co.,  274 
Premier  Electric  Co.,  274 
Riker   Electric   Motor  Co.,  274, 

280,  281 

Royal  Electric  Co.,  170 

Schorch,  276 

Schuckert   &   Co.,   49,  276,  278, 

281,  282 

Schuyler  Electric  Co.,  459 
Schwartzkopff,  L.,  see  Berliner 

Maschinenbau   Actien-Gesell- 

schaft. 
Shawhan-Th resher  Electric 

Co.,  278,  280 
Short  Electric  Railway  Co.,  282, 

283,  435 
Siemens  &  Halske  Electric  Co., 

168,  170,  273,  275,  281 
Siemens  Brothers,  272 
Simpson  Electric  Manufacturing 

Co.,  274 


Dynamos  of  various  Manufactu- 
rers— Con  tinued. 

Snell,      Albion,     see      General 
Electric  Traction  Co. 

Sperry  Electric  Co.,  458 

Sprague  Electric  Co.,  398 

Stafford  &  Eaves,  278 

Standard  Electric  Co.,  280,  458 

Stanley  Electric  Manufacturing 
Co.,  280 

Storey  Motor  and  Tool  Co.,  170, 
284 

Thomson-Houston  Electric  Co., 
277,  458,  624 

Thury,   see  Cuenod,   Sauter  & 
Co. 

Triumph  Electric  Co.,  170,  278 

United  States  Electric  Co.,  274, 
276 

Waddell-EntzCo.,  283 

Walker  Electric  Manufacturing 
Co.,  170,  280,  435 

Wenstrom  Electric  Co.,  278,  284 

Western  Electric  Co.,  276,  458 

Westinghouse  Electric  and  Man- 
ufacturing Co.,  280,  435 

Weston,  see  United  States  Elec- 
tric Co. 

Wood,  see  Fort  Wayne  Electric 
Corporation. 

Woodside  Electric  Works,  274 

Zucker  &  Levitt  &  Loeb  Co., 
281 

Zucker  &  Levitt  Chemical  Co., 
271 

Zurich  Telephone  Co.,  273,  278, 

281,  285 
Dynamotor,  see  Motor-Generator. 


Ebonite,  see  Hard  Rubber. 

Eccentricity  of  polefaces,  298 

Economic  coefficient,  see  Effi- 
ciency, Commercial. 

Eddy  current  loss  in  armature, 
calculation  of,  119-122 

Eddy  currrents  in  armature  con- 
ductors, 107,  119 

—  in   armature   core,   107,    119- 
122 

—  in  polepieces,  295 
Edge-insulation  of  armature,   79, 

82 

Edser,  Edwin  on  magnetic  leak- 
age, 262 

Effective  height  of  armature  wind- 
ing, 74 

—  of  magnet  winding,  377 


670 


INDEX. 


Effective  length  of  armature  con- 
ductor, 49 

Effects,  mechanical,  of  armature 
winding,  137-142 

Efficiencies,  average,  of  electric 
motors,  422 

Efficiency,  commercial,  or  net, 
406-409 

—  electrical,  37,  38,  39,  40,  42, 
43,  405,  406 

—  gross,  409,  410 

—  of  armature  as  an  inductor, 

135 

—  relative,    of    magnetic  field, 
211-214,  512,  533.  557.  572 

—  space-,    of    various     railway 
motors,  435 

—  weight-,  33,  410-412 

Effort,  horizontal,  of  railway  mo- 
tors, 440-442 

Electro-dynamic  force,  seat  of,  in 
toothed  armatures,  63,  64 

Electro-magnet,  see  Magnet. 

Electro-metallurgical  dynamos, 
designing  of,  459-461 

—  field-density  for,  54 

—  magnetic  density  in  armature 
of,  91,  92 

—  unipolar  forms  of,  25,  652 
Electro-motive  Force,  addition  of, 

in  closed  coil,  12 

—  allowed    for    internal  resist- 
ances, 56 

—  at  various  grouping  of  con- 
ductors, 151 

—  average,  8,  9,  19,  20,  21 

—  direction  of,  9 

—  fluctuation  of,  19 

—  magnitude  of,  6 

—  production  of,  4 
Elliptical  bore  of  field,  296 

—  magnet-cores,  289,  291 
Embedding  of   armature-conduc- 
tors,   see    Perforated    Arma- 
ture. 

Emission  of  heat  from  armature, 
126,  127 

Empirical  formula  for  heating  of 
drum  armatures,  129 

Enamel,  for  armature-insulation, 
7.8,  94 

End-insulation  of  commutator,  171 

End- rings  for  armature-core,  188, 
590 

Energy-dissipation,  see  Dissipa- 
tion of  Energy. 

Energy-loss,  specific,  in  armature, 
126-128 

—  in  magnets,  368,  371,  372 


Energy-losses  in  armature,  107- 
122 

—  in    collecting  armature   cur- 
rent, 176-180,  515 

—  in  magnets,  366,  368,  372,  375, 
383,  399,  400,  577 

Equations,  fundamental,  for  dif- 
ferent excitations,  36-43 

—  for  relative  permeance,  219- 
223 

Esson,  W.  B.,  on  capacity  of  ar- 
matures, 131 

—  on  magnetic  leakage,  262 
Evenness,  degree  of,  of  number  of 

conductors    for    series    wind- 
ings, 159-163 

Ewing,  Professor  J.  A.,  on  hys- 
teresis, no,  115 

—  on  magnetism  of  iron,  335 

—  on  permeability  of  cast-steel, 
289 

Examples,  158,  162,  167,  249-256, 
481,  488,  492,  495,  501,  505-660 

Excitation  of  field-magnetism, 
methods  of,  35 

Exploration  of  magnetic  field,  31 

—  of  magnetic  flux,  397,  398 
Exponent,  hysteretic,  116 

—  of  output-ratio,  416,  417 
External  characteristic,  476 
Extra-resistance,  383,  384,  385,  393, 

540 


Face-connection    of    drum-wound 

ring  armature,  101 
Face-insulation  of  armature-core, 

79,  82 

Face-type  commutator,  168 
Factor  of  armature  ampere-turns, 

480 

—  of  armature  reaction,  352 

—  of  brush-lead  in  toothed  and 
perforated  armatures,  350 

—  of    core-leakage    in     toothed 
and  perforated  armatures,  219 

—  of  eddy-current-loss,  120,  121, 

122 

—  of    field-deflection,    225,  230, 
231 

—  of  hysteresis-loss,  112, 113,  115 

—  of  magnetic  leakage,  215,  217- 
265 

—  of  safety,  189,  190 

Fay,   Thomas,    J.,    on     constant 

speed  motors,  427 
Feather-keys,  309 
Feldkamp  motor,  275 


INDEX. 


67I 


Fibre,   vulcanized,   for   armature- 
insulation,  79,  84,  85 
Field-area,  effective,  204,  207 
Field-bore,  diameter  of,  209,  210 
Field-density,  actual,  of  dynamo, 
202,  204,  205,  206 

—  definition  and  unit  of,  199 

—  practical  values  of,  54 
Field-distortion,  225,  230,  349,  456 
Field-efficiency,  211-213 
Field-excitation,  methods  of,  35-43 
Field-magnet  frame,  see  Magnet- 
Frame. 

Field,  magnetic,  see  Magnetic 
Field. 

—  unsymmetrical,  effect  of,  on 
armature,  140-142,  513,  534 

Finger-rule  for  direction  of  cur- 
rent and  motion,  10 

Firms,  see  Dynamos  of  various 
Manufacturers. 

Fischer-Hinnen,  J.,  on  dynamo- 
graphics,  487,  497,  500 

—  on   prevention  of    armature- 
reaction,  464 

Fitted  contact,  182,  183 

Fittings  (brush  holders,  conveying 

parts,  switches,  etc.),  181-183 
Flanges  for  magnet-cores,  308,  523, 

542,  576,  595,  650 

—  on  field-frames,  287 
Flat-ring  armatures,  93 
Fleming,  Professor  J.  A.,  on  eddy 

current  loss,  121 

—  on  rule   for  direction  of  cur- 
rent, 10 

Flow  of  magnetic  lines,  see  Flux. 

Fluctuations  of  E.  M.  F.  of  corn- 
mutated  currents,  14-21 

Flux-density,  magnetic,  in  air- 
gaps,  54 

—  in  armature-core,  91 

—  in  magnet-frame,  313 

Flux,  distribution  of,  in  dynamo, 

397-399 

—  magnetic,  199,  331 

—  total,  of  dynamo,  214,  257-261 

—  useful,    of  dynamo,  92,    133, 
200-202,  211-214 

Foppl,  A.,  on  hollow  magnet- 
cores,  292 

Forbes,  Professor  George,  on 
leakage  formulae,  216 

—  on   prevention   of    armature- 
reaction,  465 

Force,  attractive,  of  magnetic 
field,  140,  141,  513,  534 

—  electro-dynamic,    in    toothed 
armatures,  63,  64 


Force,  Electro-Motive,  see  Elec- 
tro-motive Force. 

—  horizontal,  exerted  by  railway 
motor,  440-442 

—  magnetizing,    see    Magnetiz- 
ing Force. 

—  peripheral,   of  armature-con- 
ductors, 138-140,  188,  513,  534 

—  thrusting,  on  armature,  140- 
142,  513,  534 

—  tangential,  at  pulley-circum- 
ference, 193,  287 

—  due  to  brush-friction,  179,  515 
Ford,    Bruce,   on  unipolar    dyna- 
mos, 25 

Forged  steel,  448,  450 
Forms  of  cross-section  for  magnet- 
cores,  289-291 

—  of  dynamo-brushes,  172-174 

—  of  field  magnet  frames,  269- 
287 

—  of  fields  around  ring    arma- 
ture, 98 

—  of  polepieces,  30,  295-299 

—  of  slot-insulation  for  toothed 
and  perforated   armatures,  81 

—  of     unsymmetrical       bipolar 
fields,  142 

Formulas  for  dimensions,  wind- 
ing data,  etc.,  see  Dimensions, 
Diameter,  Length,  Breadth, 
Sectional  Area,  Number,  etc. 

—  fundamental,  7,    8,  9,  36-43, 
55,  57,  200,  201,  219,  314,  334, 

377,  385 
Foucault  currents,  see  Eddy  Cur- 

ents. 

Four-coil  armature,  17,  18 
Fourpolar    double    magnet  type, 

240,  270,  285 

—  iron-clad  type,   236,  255,  263, 
270,  284,  603 

Frame,  see  Magnet  Frame. 
Frequency,  no,  in,  119,   120,  121 
Friction,  losses  by,   406-409,  526, 

546,   565,    578,   602,    636,    643, 

651 

—  of  commutator-brushes,  176- 
180 

Fringe  of  magnetic  field,  29,  30 

Frisbee,  Harry  D.,  on  distribution 
of  magnetic  flux,  397 

Front-pitch  of  magnetic-winding, 
159-167 

Fundamental  calculations  for  ar- 
mature winding,  47-57 

—  equations  for  different  excita- 
tions, 36-43 

—  permeance  formula,  219 


672 


INDEX. 


Gap,  see  Air  Gap. 
Gap-circumference,   effective,  135 
Gauges  of  wire,  103,  367 
Gauss,  the  unit  of  magnetic  den- 
sity, 199 

Gauze  brushes,  171,173 
Gearing  of  railway  motors,  433- 

435 

Gearless  railway  motors,  434 

Generation  of  E.  M.  F.,  4,  5,  22, 
47.  48 

Generator,  electric,  definition  of,  3 

"  Giant  "  dynamo,  272 

Gilbert,  the  unit  of  magnetomo- 
tive force,  333 

Grade  of  railway  track,  440,  441 

Graphic  methods  of  dynamo-cal- 
culation, 476-502 

Grawinkel  &  Strecker,  on  forms 
of  field-magnets,  273,  274,  275, 
276,  278,  281,  282 

Griscom  motor,  276 

Grotrian,  Professor,  on  hollow 
magnet-cores,  291 

Grouping  of  armature-coils,  147- 

155 

—  of  magnetic  circuits,  353-356 
Gun-metal,  169 


H 


Hard  rubber,  85 

Hardness,  magnetic,  no 

Heads  in  drum-armatures,  size  of; 

123,  124 
Heat,  effect  of ,  on  hysteresis,  117, 

118 

—  on  insulation-resistance,  85 
Heat,  radiation  of,  from  armature, 

126,  127 

Heating  of  armatures,    127,    129, 
130,  132 

—  of  magnet-coils,  368-371 
Height  of  armature  winding,   70, 

7i,  74,  75 

—  of  magnet  winding,  317,  361, 
371,  375,  377,  386,  387 

—  of  polepieces,  326 

—  of  zinc  blocks,  301-303,  536 
Hering,   Carl,  on  unipolar   dyna- 
mos, 25 

Herrick,  Albert  B.,   on  insulating 

materials,  86 

Heteropolar  induction,  23,  26 
High-potential  dynamos,  462,  463 
High-speed  dynamos,   52,   60,  91, 

132,  134,  136,  185,  187,  192,  193 


Hill,  Claude  W.,  on  strength  of 
reversing  field,  471 

Hobart,  H.  M.,  on  armature  wind- 
ing, 156 

Holes  in  core-discs,  see  Perforated 
Armature. 

Hollow  magnet-cores,  290-292 

Homopolar  dynamos,  see  Unipolar 
Dynamos. 

Hopkinson,  Dr.  J.,  on  hysteresis, 
no 

Hopkinson,  J.  &  E.,  on  magnetic 
leakage,  262 

Horizontal  effort  of  railway  mo- 
tors, 438-442 

—  magnet  types,   238,  239,  245, 
246,  251,  253,  254,  263,  269,  270, 
273,  275,  276,  277,  284,  285 

Horns  for  driving  drum  armatures, 
73,  140 

—  of  polepieces,  see  Pole-Tips. 
Horsepower,  the  unit  of  work,  137 
Horseshoe  types,  leakage  factors 

of,  249-251,  252-254,  263 

—  permeance  across  polepieces 
in,  238,  242 

—  permeance  between  magnet 
cores  in,  231-233 

—  permeance      between     pole- 
pieces  and  yoke  in,  245,  246 

Huhn,  George  P.,  on  distribution 

of  potential,  32 
Hysteresis,  definition  of,  no 

—  variation  of,  with  density  of 
magnetization,  116 

—  variation  of,   with    tempera- 
ture, 118 

Hysteresis-heat, specific, in  toothed 
armatures,  69 

Hysteresis-loss  in  armature,  cal- 
culation of,  107,  109-118,  591 

Hysteretic  exponent,  116 

—  resistance,  no,  in 


I 


Ideal  position  of  brushes,  29 
Impurities  in  cast  steel,  288,  289 
Incandescent    generators,     large, 

field-densities  for,  54 
— "magnetic  density  in  armature 

of,  91 

—  shunt-excitation  of,  39 
Inclined  magnet  types,   232,  269, 

276 
Induction,  electro-magnetic,  3,  5, 

22,  23,  47,  48,  405,  423 
Inductor,  see  Conductor. 
Ineconomy  of  small  dynamos,  472 


INDEX. 


673 


Innerpole  types,  131,  168,  263,  264, 
269,  270,  281,  282,  287,  566,  580 

Insulating  materials,  properties  of, 
83-86 

Insulation,  between  laminae  of 
armature  core,  93,  94 

—  of  armature,  resistance  of,  86, 
5io 

—  of  armature,  thickness  of,  82 

—  of  commutator-bars,  171 

—  of  magnet-cores,  thickness  of, 

543,  565,  576 

—  weight  of,   on  round  gauge 
wire,  103 

Intake  of  motor,  405,  420 
Integrated  curve  of  potentials,  32, 

33 

Intensity,  see  Density. 
Intermittent    work,    motors     for, 

429-431,  637 

Internal  characteristic,  476 
Inventors,  see  Dynamos  of  various 

Manufacturers. 
Inverted  horseshoe  type,  240,  241, 

246,  250,  263,  264,  269,  272,  286, 

299,  614 
Iron-clad  types,    classification  of, 

269,  270,  277,  '278,  284 

—  leakage-factor  for,  255,  256,263 

—  permeance  across  polepieces 
in,  243 

—  permeance  between   magnet 
cores  in,  234-237 

—  permeance      between      pole- 
pieces  and  yoke  in,  247 

Iron,  for  armature-cores,  93,  94,  no, 
113,  115,  118,  119,  120,  121,  122 

—  for    magnet-frame,    30,     288, 
289,  293,  294,  300,  305-309 

—  hysteretic  resistance  for  vari- 
ous kinds  of,  in 

—  permeability  of  different  kinds 
of,  310-313 

—  projections,  effect  of,  in  mag- 
netic field,  64 

—  specific    magnetizing     forces 
for  different  kinds  of,   336-338 

—  wire,  for  armature-,  and  mag- 
net winding,  472-475 

—  wire,  for  armature-cores,  93, 

94,  no,  113,  115 

Ives,  Arthur  Stanley,  on  magnetic 
leakage,  262 


Jackson,  Professor  Dugald  C.,  on 

ratio   of  tnagnet-  to  armature 
cross-section,  292,  293 


Japan  (enamel)  for  armature-insu- 
lation, 78,  94 

Joints  in  magnetic  circuit,  305-309 

Journals,  calculation  of,  184,  186, 

187,  190,  191,  192,  303-305,  516 

—  friction  in,  406-409,  526,  546, 

565,  578,  602,  636,  643,  651 


K 


Kapp,  Gisbert,  on  diametral  cur- 
rent density  of  armature,  133 

—  on  magnetic  leakage,  216 

—  on  permeability  of  cast  steel, 
289 

Kelvin,   Lord,   see  Thomson,    Sir 

William 
Kennedy,    Rankine,   on  shape  of 

polepieces,  299 
Kennelly,   A.  E.,  on    magnetism 

of  iron,  335 

—  on    seat    of    electro-dynamic 
force  in  iron-clad  armatures,  64 

"  King"  dynamo,  271 

Kittler,  Professor  Dr.  E.,  on  forms 
of  field  magnets,  273,  275,  276, 
277,  281,  282,  283,  285 

Klaasen,  Miss  Helen  G.,  on  hys- 
teresis, 115  . 

Knee  of  saturation  curve,  312 

Knight,  Percy  H.,  on  magnetism 
of  iron,  335 

Kolben,  Emil,  on  railway  motor 
construction,  431 

—  on  worm-gearing  for  electric 
motors,  434 

Kunz,  Dr.  W.,  on  hysteresis,  116 


Lag,  angle  of,  30,  421 

Lahmeyer,  W.,  on  magnetic  leak- 
age, 262 

Laminated  joint,  182 

Lamination  of  armature  core,  93, 
94,  119-122 

—  of  polepieces,  297 

Lap-,   or  loop-,  winding,  144,  145, 

152 
Law  of  armature-induction,  47,  48, 

49 

—  of  conductance,  219 

—  of  cutting  lines  of  force,  47, 
200 

—  of  hysteresis,  no 

—  of  magnetic  circuit,  331 

—  Ohm's,  36,  41,  384,  393 
Layers,    number  of,    of  armature 

wire,  74,  508 


674 


INDEX. 


Lead  of  brushes, '30,  349,  350,  421 
Leads  for  current,    181-183,   379, 

524 

Leakage,  magnetic,  calculation 
of,  from  dimensions  of  frame, 
217-256 

—  calculation  of,  from  machine- 
test,  257-265 

—  in  toothed  armatures,  53,  218, 
219 

Leather,  safe  working  strength 
of,  193 

Leatheroid,  for  armature-insula- 
tion, 79,  85 

Lecher,  Professor,  on  unipolar 
dynamos,  25 

Length  of  armature-conductor,  55, 
95-100 

—  of  armature-bearings,  190-192, 
5i6 

—  of  armature-core,  76 

—  of  armature-shaft,  184 

—  of  commutator  brush -surf  ace, 
168,  176,  515 

—  of  heads  in  drum  armatures, 
123,  124 

—  of  magnet-cores,  316-319 

—  of  magnetic  circuit,  224,  230, 
243,  347.  348- 

—  of  magnet- wire,  360 

—  of  mean  turn    on    magnets, 
374 

Liberation  of  heat  from  armature, 

126,  127 
Limit  of  armature  capacity,  132- 

135 

—  of  magnetization,  313 

Line,  neutral,  of  magnetic  field, 

225,  459 
Line-potential  for  railway  motor, 

442 
Lines  of  force,  cutting  of,  3,  5,  6, 

8,  9,  12,  22,  27,  47,  48,  52,  200, 

201 

—  definition  and  unit  of,  199 
Linseed  oil;  for  armature-insula- 
tion, 83,  85 

Load-limit  of  armature,  132-135 
Long  connection  type  of    series 
armature  winding,  157,  158 

—  shunt  compound  winding,  41, 
42 

Loop  winding,  see  Lap  Winding. 
Losses  in  armature,  107-126 

—  in  bearings,  406-409,  526,  546, 
565,  578,  602,  636,  643,  651 

—  in  belting,  409 

—  in  commutator-brush-contact, 
175,  176-180 


Low-speed   dynamos,    52,    61,    91,, 
132,  134,  136,  185,  187,  192 

Lubrication  of  bearings,  305 
—  of  commutator,  177,  179 

Lugs  for  connecting  cables,  181, 
182 


M 


Magnet-cores,     dimensioning    of, 
316-324 

—  general     construction     rules 
for,  288-293 

—  relative   average    permeance 
between,  231-238 

Magnet-frame,    classification      of 
types  of,  269,  270 

—  dimensioning  of,  313-327 

—  general  design  of,  288-309 

—  magnetizing  force   for,    344- 
348 

Magnetic  circuit,  air-gap    in,  see 
Air-Gaps. 

—  joints  in,  305-309 

—  law  of,  331 

—  reluctance  of,  331 
Magnetic  field,  definition  and  unit 

of,  199 

—  exploration  of,  31 

—  fringe  of,  29,  30 

—  motion  of  conductor  in,  5 

—  relative  efficiency  of,  211 
Magnetic  flux,  see  Flux,  Magnetic. 

—  intensity,  see  Density,  Mag- 
netic. 

—  leakage,  see  Leakage,   Mag- 
netic. 

—  permeability,  see  Permeabil- 
ity. 

—  pull  on  armature,  see  Arma- 
ture-Thrust. 

—  reluctance,  see  Reluctance. 

—  units,  definition,  of,  199 
Magnetization,  absolute  and  prac- 
tical limits  of,  313 

—  influence  of,  on  brush-lead  in 
iron-clad  armatures,  350 

—  influence  of,  on  hysteretic  ex- 
ponent, 116 

—  influence  of,  on  magnetizing 
force,  336,  337 

Magnetizing    force    for    air-gaps, 
339.  340 

—  for  any  portion  of  a  circuit, 
333-338 

—  for  armature-core,  340-343 

—  for  compensating    armature- 
reaction,  348-352 

—  for  field-frame,  344-348 


INDEX. 


675 


Magnetomotive  force,  331 
Magnet-winding,    calculation    of, 
359-401,  450,  451,  486-497,  522, 
540,  549.  562,  576,  599.  6l2.  635, 
640,  649,  654,  659 

—  methods  of  excitation  of,  35- 

43 

"  Manchester  "  dynamo,  276 
Manganese,  in  cast  steel,  288,  289 
Manufacturers,    see   Dynamos  of 

various  Manufacturers. 
Martin    &  Wetzler,    on    electric 

motors,  270 
Mass   of    iron    in    armature  core, 

no,  in,  112,  114,  119,  120 
Materials  for  armature  core,  93 

—  for  armature  insulation,  83-86 

—  for  commutator,  169 

—  for  dynamo-base,  299,  300 

—  for  magnet-cores,  288 

—  for  polepieces,  53,  296 
Mavor,  on  magnetic  leakage,  264 
Maximum  efficiency,  current  for, 

of  motors,  428,  429,  642 

—  electrical,   of  shunt-dynamo, 
39.  40 

—  safe    capacity    of    armature, 

.132-135 

MeanE.  M.  F.,  21 

Mechanical  calculations  about  ar- 
mature, 184-195,  516,  517 

—  effects  of  armature-winding, 
137-142,  513,  534 

Merrill,  E.  A.,  on  capacity  of  rail- 
way motors,  438 

Metallurgical  dynamos,  see  Elec- 
tro-Metallurgical Dynamos. 

Mho,  unit  of  electrical  conductiv- 
ity, 119 

Mica,  for  armature-insulation,  78, 
79-  83,  85 

—  for       commutator-insulation, 
170,  171 

Micanite  (cloth,  paper,  plate),  for 
armature-insulation,  80,  81,  84, 
85 

Mitis  iron,  in,  294,  312,  313 

Mixed  armature  winding,  144,  147 

Monell,  A.,  on  effect  of  tempera- 
ture on  insulating  materials, 
86 

Mordey,  W.  H.,  on  prevention  of 
armature-reaction,  465 

Motion,  relative,  between  conduct- 
ors and  magnetic  fields,  3,  4- 
12 

Motor,  electric,  calculation  of, 
419-442,  628-652 

—  definition  of,  3 


Motor-generators,  calculation  of-,- 
452-454,  655 

Multiple  circuit  winding,  see  Par- 
allel Winding. 

Multiplex,  or  multiple,  winding, 
149,  150,  151,  160,  165 

Multipolar  dynamos,  classification 
of,  269,  270,  279  -285,  287 

—  connecting  formula  for,  154, 

155  f 

—  economy  of,  33 

—  field-densities  for,  54 

—  kinds  of  series  windings  pos- 
sible for,  156 

—  number  of  brushes  for,  34,  102 

—  permeance  across  polepieces 
in,  243,  244 

—  permeance   between   magnet 
cores  in,  233,  234 

—  permeance     between      pole- 
pieces  and  yoke  in,  247,  248 

Multipolar  types,  practical  forms 
of,  279-285 

Munroe  and  Jamieson,  on  insula- 
tion-resistance of  wood,  85 

Muslin,  for  armature-insulation, 
79,  85 


N 


Negbauer,  Walter,  on  magnetism 
of  iron,  335 

Net-efficiency,  see  Efficiency,  Net. 

Neutral  points  on  commutator, 
148,  459 

Normal  load,  calculation  of  mag- 
netizing force  for,  396 

Number  of  ampere-turns,  333-352 

—  of  armature  circuits  in  multi- 
polar  dynamos,  49,  104 

—  of   armature   conductors,  76, 
77.  159-163 

—  of  armature  divisions,  90 

—  of  brushes  in  multipolar  ma- 
chines. 34,  102 

—  of  coils  in   armature,    15-2.1, 
87,  90,  153-155.  158-163 

—  of  commutator  divisions,  87, 
88 

—  of  convolutions  per  commu- 
tator division,  89 

—  of    cycles    of  magnetization, 
no,  in,  112,  119,  121 

—  of  layers  of  wire  on  armature, 
74.  508 

—  of  lines   of  force  per  square 
inch,  54,  91 

—  of  pairs  of  magnet  poles,  48, 
5i,  53 


676 


INDEX. 


Number  of  reversals  of  E.  M.  F.  in 
one  revolution  of    conductor, 

22,  23 

—  of  revolutions   of  .armature, 
58,  60,  61 

—  of  slots  in  toothed  and  per- 
forated armatures,  65,  66,  70, 

7i 

—  of  useful  lines  of  force,  7,  9, 

92,   133,  200-202,    2II-2I4 

—  of  wires  per  layer  on  arma- 
ture, 72,  73,  74 


Oersted,  the  unit  of  magnetic  re- 
luctance, 333 

Ohm's  law,  36,  41,  384,  393 

Oiled  fabrics  (paper,  cloth,  silk) 
for  armature  insulation,  78,  85 

One-coil  armature,  15,  20 

One-material  magnet  frame,  cal- 
culation of  flux  in,  259,  614, 
618,  624 

—  joints  in,  305,  306,  307 
Open  circuit,  calculation  of  mag- 
netizing forces  for,  395 

Open-coil  winding,  143,  144,  458 
Ordinary  compound  dynamo,  41 
Outer-inner-pole  type,  270,  283 
Outerpole  types,  269,  270,280,  281, 

287,  304 
Output,  formulae  for,  405,  420,  438 

—  maximum,  of  armature,   132- 
135 

—  of  dynamo  as  a  function  of 
size,  416-418 

Oval  magnet  cores,  232,  234,  289, 
291,  318,  322,  374 

Over-compounding,  43,  396 

Over-type,  272,  278,  304 

Owens,  Professor  R.  B.,  on  closed 
coil  arc  dynamo,  455 

Oxide  coating  for  insulating  ar- 
mature-laminae, 93,  94 


Paper,  for  armature  insulation,  78, 
85.  94 

Paraffined  materials,  for  armature 
insulation,  83,  85 

Parallel,  or  multiple  circuit,  arma- 
ture winding,  148,  151,  152, 
154 

Parchment,  for  armature  insula- 
tion, 85 

Parmly,  C.  H.,  on  unipolar  dyna- 
mos, 25 


Parshall,  H.  F.,  on  armature  wind 
ings,  156 

—  on  use  of  steel  in  dynamos,  288 
Pedestals  for  dynamos,  142,  303 
Perforated  armatures,  advantages 

and  disadvantages  of,  61,  62, 

63 

—  core-leakage  in,  53,  218,  219 

—  definition  of,  4 

—  dimensioning  of,  71,  72 

—  effective  field  area  of,  207 

—  insulation  of,  8 1 

—  percentage  of  effective  gap- 
circumference  for,  135 

—  percentage  of  polar  arc  for,  50 
Peripheral  force  on  armature-con- 
ductors, 138,  139 

—  on  pulley,  193 

Peripheral  speed  of  armature,  52, 

—  of  pulley,  193 
Permeability  of  iron,  310-312 
Permeance,  law  of,  219 

—  relative,     across    polepieces, 
238-244 

—  relative      average,     between 
magnet  cores,  231-238 

—  relative,  between  polepieces 
and  yoke,  244-248 

—  relative,  general  formulae  for, 
220-223 

—  relative,  of  air-gaps,  224-230 
Permissible  current  densities,  180 
Permissible  energy-dissipation,  in 

armature,  127 

—  in  magnets,  372 

Perry,  C.  L.,  on  effect  of  tempera- 
ture on  insulating  materials, 
86 

"  Phoenix"  dynamo,  614 
Phosphor-bronze,  169,  189,  434 
Phosphorus,  in  cast  steel,  288 
Physical    principles    of    dynamo- 
electric  machines,  3-43 
Picou,  on  E.  M.   F.  of  shunt  dy- 
namo, 485 
Pierced  core-discs,  see  Perforated 

Armatures. 
Pitch  of  armature-conductors,  414, 

4i5 

—  of  armature-winding,  152-167 

—  of  slots  in  toothed  armatures, 

65.  7i 

Plating  dynamos,  see  Electro-Met- 
allurgical Dynamos. 

Plugs,  for  switch  connections,  182, 

183 

Points,  neutral,  on  commutator, 
148 


INDEX. 


677 


Polar  arc,  percentage  of,  49,  203, 

207,  210 

Pole-armature,  see  Star- Armature. 
Pole-bridges,  296 
Pole-bushing,  49,  296 
Pole-corners,  207,  208,  298 
Pole-faces,  eccentricity  of,  298 
Pole-shoes,  bore  of,  209,  210 

—  construction-rules    for,    293- 
299 

—  dimensioning  of,  325-327 

—  magnetic  circuit  in,  346,  348 
Pole-strength,  unit  of,  199 
Pole-surface,  127,  128,  204 
Pole-tips,  296,  298 

Poole,  Cecil  P.,  on  simplified 
method  of  armature  calcula- 
tion, 413 

Position  of  brushes,  ideal,  29 
Potential,  distribution  of,  around 
armature,  31-33 

—  magnetic,  224 

Power  for  driving  generator,  420 

—  for  propelling  car,  440-442 
Power-transmission,  dynamos  for, 

Qi,  497 
Practical  field  densities,  54 

—  limit  of  magnetization,  313 

—  values  of  armature  induction, 
50 

—  working  densities  in  magnet 
frame,  313 

Press-board,  for  armature  insula- 
tion, 78,  79,  80,  85 

Pressure,  best,  of  commutator 
brushes,  176-179,  515 

—  effect  of,  on  joints,  306,  307 

—  electric,    see    Electro-Motive 
Force. 

Prevention  of  armature-reaction, 
463-470 

—  of  armature-thrust,  298 

—  of  crowding  of  lines  in  pole- 
pieces,  295,  296 

—  of   eddy    currents    in     pole- 
pieces,  297 

—  of  sparking,  30,  62,  172,  173, 
297,  298,  299,  459,  465,  471,  472 

—  of  vibration,  287,  299,  431 
Principles,   physical,   of  dynamo- 
electric  machines,  3-43 

Production  of  continuous  current, 
13,  14,  22 

—  of  E.  M.  F.,4,  5,  47,  48 
Projecting  teeth,  76,  134,  219,  228, 

229 

Projections  of  magnet-frame,  294 
Puffer,    Professor,    on      magnetic 

leakage,  262 


Pull,  see  Force. 

Pulley,  calculation  of,  191,  195 


Quadruple  magnet  type,  270,  285, 
299 

Quadruplex  armature  winding, 
150 

Quadruply  re-entrant  armature- 
winding,  150 

Qualification  of  number  of  con- 
ductors for  various  windings, 
157-167 


Radial  clearance  of  armature,  209 

—  depth  of  armature  core,  92 

—  multipolar  type,  243,  248,  269, 
280,  281,  566,  587,  624,  644 

Radiating  surface  of  armature, 
122-126 

—  of  magnets,  369 
Radiation  of  heat  from  armature, 

126,  127 
Radi-tangent  multipolar  type,  270, 

282 
Railway-generators,     adjustment 

of  carbon  brushes  in,  172 

—  magnetic  density  in  armature 
of,  91 

—  toothed  armatures  for,  62 
Railway-motors,     calculation    of, 

438-442,  500-502 

—  general  data  of,  435 

—  magnetic  density  in  armature 
of,  91 

Randolph,  A.,  on  unipolar  dyna- 
mos, 25 

Ratio  of  armature-  to  field  ampere- 
turns,  349 

—  of  clearance  to  pitch  in  slotted 
armatures,  230 

—  of  core-diameter  to  winding 
diameter  of  small  armatures,  59 

—  of  height  of  zinc   blocks  to 
length  of  gaps,  301,  302 

—  of  length  to  diameter  of  drum 
armatures,  96,  97 

—  of  length  to  diameter  of  mag- 
net-cores, 320-322 

—  of  magnet-,  to  armature  cross- 
section,  292,  293 

—  of  mean  turn  to  core  diameter 
of  cylindrical  magnets,  375 

—  of    minimum     to    maximum 
width  of  tooth  in  iron  clad  ar- 
matures, 592 


6y8 


INDEX. 


Ratio  of  net  iron  section  to  total 
cross-section  of  armature- 
core,  94 

—  of  pole-area  to  armature  radi- 
ating surface,  127 

—  of  pole-distance  to  length  of 
gaps,  208 

—  of  radiating  surface  to  core 
surface  of  magnets,  371 

—  of  shunt-,  to  armature-resist- 
ance, 40 

—  of    speed-reduction,    of    rail- 
way motors,  433,  435 

—  of  transformation,  of  motor- 
generators,  454,  656 

—  of  width  of  slots  to  their  pitch 
on    armature    circumference, 
219,  230 

—  of  winding-height  to  diame- 
ter of  magnet  core,  317,  371 

Reaction  of  armature,  see  Arma- 
ture-Reaction. 

Rectangular  magnet-cores,  233, 
289,  291,  318,  321,  369,  374 

Rectification  of  alternating  cur- 
rents, 13,  14 

Re-en trancy  of  armature-winding, 
150 

Regenerative  armatures,  reversi- 
ble, 467 

Regulation  of  arc  lighting  dyna- 
mos, 458,  459 

—  of  railway  motors,  436,  437 

—  of  series  dynamos,    377-382, 


523-526 
—  of 


shunt  dynamos,    390-394, 

487-497 

Reid,  Thorburn,  on  railway  mo- 
tor calculation,  438 

Relation  between  brush-lead  and 
density  of  lines  in  armature- 
teeth,  350 

—  between     core-leakage     and 
shape  of  slots  in  toothed  ar- 
matures, 219 

—  between  effective  gap  circum- 
ference  and    polar  embrace, 
135 

—  between   electrical  efficiency 
and  ratio  of  shunt-  to  armature 
resistance,  40 

—  between  fluctuation  of  E.  M. 
F.  and  number  of  commuta- 
tor divisions,  19 

—  between  horizontal  effort  and 
grade, 441 

—  between   size   and   output   of 
dynamos,  416-418 

—  between  temperature  increase 


and     peripheral    velocity    of 
armature,  127,  128 
Relation     between     temperature 
increase   and   winding   depth 
of  magnets,  371 

—  between   total   length  of  ar- 
mature    wire     and     ratio    of 
length  to  diameter  of  core,  96 

Reluctance,  331 
Reluctivity,  331 

Resistance,  hysteretic,  of  various 
kinds  of  iron,  in 

—  insulation-,  of  various   mate- 
rials, 85 

—  internal,  of  dynamo,  E.  M.  F. 
allowed  for,  56 

—  of  armature-winding,  102-106 

—  of  magnet-winding,  375,  376, 
384,  388,  399,  400 

Resistance-method  of  speed-con- 
trol for  railway  motors,  436 

Reversing  field,  strength  of,  471, 
4.72 

Rheostat  for  regulating  series  dy- 
namos, 377-382,  523-526 

—  for  regulating    shunt    dyna- 
mos, 390-394,  487-497,  543-546 

—  for  starting  motors,  424 
Ribbon  armature-cores,  93 

—  copper-,  for  series  field  wind- 
ing, 36,  376 

Ring-armatures,  bearings  for,  192 

—  core-densities  for,  91 

—  definition  of,  4 

—  diameters  of  shafts  for,  187 

—  drum-wound,  35,  89,  99,  100, 

165 

—  height  of  winding  space  in,  75 

—  insulation  of,  80,  81 

—  radiating  surface  of,  125,   126 

—  speeds  and  diameters  of,  60, 
61 

—  total  length  of  conductor  on, 
98,  99 

Ring-winding,  see  Spiral  Wind- 
ing. 

Robinson,  F.  Gge.,  on  disruptive 
strength  of  insulating  mate- 
rials, 86 

Rockers,  527 

Rotary  transformer,  see  Motor- 
Generator. 

Rotation,  direction  of,  in  genera- 
tor, 10 

—  in  motor,    422,  423 

Round  magnet  cores,  see  Cylin- 
drical Magnets. 

Rubber,  for  armature-insulation, 
78,  83,  85 


INDEX. 


679 


Rule,    for    connecting    armature 
coils,  152 

—  for  direction  of  current,  10 

—  for  direction  of  motion,  10 
Running  value  of  armature,   135, 

136 

Ryan,     Professor     Harris    J.,    on 
shape  of  polepieces,  298 

—  on  prevention  of    armature- 
reaction,  464 


Safe  capacity  of  armature,  132-135 

—  peripheral   velocities   of  uni- 
polar armatures,  448 

—  working  strain  of  materials, 
189,  193 

Safety,  factor  of,  189,  190 
Salient  poles,  275 
Saturation,  magnetic,  312,  313,  338 
Sayers,  W.  B.,  on  driving  force  in 
toothed  armatures,  63 

—  on   prevention   of    armature- 
reaction,  467 

Schulz,  Ernst,  on  cast  steel  mag- 
net frames,  289 

—  on  heating    of    drum   arma- 
tures, 129 

—  on  hollqw  magnet  cores,  292 

—  on    lamination    of    armature 
core,  93 

Screwed  contact,  182,  183 
Screw-stud,  308 

Sectional   area   of    armature-con- 
ductor, 57 

—  of  armature-core,  92 

—  of  magnet-frame,  313-316 

—  of  magnetic  circuit,  204,  230, 
341,  345,  346 

—  of  magnet-wire,  363 

—  of  slots  in  toothed  and  per- 
forated armatures,  71 

Selection  of  insulating  material,  83 

—  of  magnet-type,  285-287,  437 

—  of    wire    for    armature    con- 
ductor, 57,  506,  528,    567,   588, 
638,  645 

—  of  wire  for  magnet-winding, 
376,  386,  400,  523,  541,  549,  587, 

599.  649 

Self-induction,  29,  62,  172,  297,  465 
Self-oiling  bearings,  305 
Series  dynamo,  efficiency  of,    37, 

405,  407 

—  E.  M.  F.  allowed  for  internal 
resistance  of,  56 

—  fundamental  equations  of,  36, 
37 


Series  motor,   406,   408,  428,  429^ 
436,  628 

Series,   or  two-circuit,   armature- 
winding,  148,  151,  153,  155-164 

Series-parallel  armature-winding, 

148,  153 

—  control  of  railway  motors,  437 
Series-winding,     calculation     of, 

3747382,  522,  586,  635 
—  principle  of,  36,  37 
Sever,    George    F.,    on    effect  of 

temperature     on      insulating 

materials,  86 
Shaft,  calculation  of,  184-186,  516 

—  insulation  of,  79,  82 
Shape,  see  Form. 

Sheet  iron,  for  armature  cores,  93, 

94,   IIO,   113,    115,    120,    I2If   122 

Shellaced  materials,  for  armature 

insulation,  85 
Short-circuiting  of  armature-coils, 

28,  30,  149,  174,  175,  298 
Short  connection     type   of    series 

winding,  157,  158 
Short,    Professor   Sidney    H.,  on 

gearless  railway  motors,  434 
Shunt-coil     regulator     for    series 

winding,  377-382,  523-526 
Shunt-dynamo,    efficiency   of,    38, 


39,  40,  406,  407,  408 


M.  F.  allowed  for  internal 
resistance  of,  56 

—  fundamental  equations  of,  38, 
39,  40 

—  total  armature  current  in,  109 
Shunt,     magnetic,     across     pole- 
pieces,  296 

Shunt-motor,  406,  408,  426,  427, 
428,  429,  637 

Shunt-resistance,  ratio  of,  to  ar- 
mature-resistance for  differ- 
ent efficiencies,  40 

Shunt-winding,  calculation  of, 
383-394.  541,  576,  612,  640,654, 
659 

—  principle  of,  37-40 
Side-insulation  of  commutator,  171 
Silicon,  in  cast  steel,  288,  289 
Silk-covering  of  wires,  weight  of, 

103 

Silk  for  armature  insulation,  78,  85 
Simplex,  or  single,  armature-wind- 
ing, 149,  150,  151,  156,  157,  159, 
164,  165 

Simplified  method  of  armature- 
calculation,  413-416 

—  process  of  constructing  mag- 
netic characteristic,  480 

Sine  curve,  13,   20 


68o 


INDEX. 


Single  horseshoe  type,  classifica- 
tion of,  269,  270-273 

—  magnetic  leakage  in,  231,  232, 
239,  240,  241,  245,  246,  249,  250, 
251,  263 

Single  magnet  iron-clad  type,  237,. 
263,  269,  278 

—  multipolar    types,    263,    270, 
283,  580 

—  ring  type,  269,  275 

—  type,    classification    of,    269, 

273-275 

—  type,    magnetic    leakage  in, 
241,  242,  251,  252,  263 

Singly  re-entrant  armature-wind- 
ing, 150,  156,  160, 161,  162, 163, 
164,  167 

Sinusoid,  13 

Size,  see  Dimensions. 

Skeleton  pulleys,  for  driving  ring 
armatures,  186,  188-190 

Skinner,  C.  A.,  on  closed  coil  arc 
dynamo,  455 

Slanting  pole-corners,  296,  460 

Sliding  contact,  current  density 
for,  183 

Slotted  armatures,  see  Toothed 
Core  Armatures. 

Slotting  of  polepieces,  297 

Smooth  core  armatures,  definition 
of,  4 

—  effective  field  area  of,  204 

—  factor  of  field-deflection  for, 
225 

—  gap-permeance  of,  224-227 

—  height  of  binding- bands  on, 
75 

—  height  of  winding  space  in, 
75 

—  percentage  of  effective  gap 
circumference  for,  135 

—  percentage  of  polar  arc  for, 
49 

Sources  of  energy-dissipation  in 
armature,  107 

—  of     magnetomotive       force, 
grouping  of,  353,  354 

—  of  sparking,  see  Sparking. 
Space-efficiency    of    railway    mo- 
tors, 435 

Spacing  of  armature-connections, 
see  Pitch  of  Armature-Wind- 
ing. 

Span,  polar,  see  Polar  Arc. 

Sparking,  29,  30,  62,  172,  173,  297, 
298,  299,459 

Specific  armature  induction,  51 

—  energy-loss  in  armature,  126 

—  energy-loss  in    magnets,  372 


Specific     generating     power     of 

motor,  425,  636,  642,  651 
— magnetizing  force,  334-338 

—  resistance  of  insulating  ma- 
terials, 85 

—  temperature    increase   in  ar- 
mature, 127 

—  temperature  increase  in  mag- 
net-coils, 371 

—  weight  and  cost  of  dynamos, 
412 

Speed,  see  Velocity. 

Speed-calculation  of  electric  mo- 
tors, 424-427,  636,  642,  651 

Speed  regulation  of  railway  mo- 
tors, 436,  437 

Speeds,  table  of,  for  armatures, 
60,  61 

Spherical  bearings,  304 

Spiders  for  ring  armatures,  140, 
186,  188-190 

Spiral  winding,  or  ring  winding, 
144,  152,  154,  189 

Spokes  for  ring  armatures,  186, 
188-190,  516 

Spools  for  magnet-cores,   359-363, 

543.  55i 

Sprague  motor,  398 
Spread,  lateral,  of  magnetic  field, 

529 

Spring  contact,  181,  183 
Spur  gearing,  433,  435 
Square  wire,  for  armature-core,  94 
Stansfield,    Herbert,  on  magnetic 

leakage,  262 

Star  armature,  definition  of,  4 
"  Star  "  dynamo,  273 
Starting  resistance,  424 
Stationary    motor,      see     Motor, 

Electric. 
Steel,  for  armature-shafts,  184-186 

—  for  magnet-frame,    288,    289, 

293 

—  safe  working  load  of,  189 
Steinmetz,     Charles    P.,    on    arc 

lighting  dynamos,  455 

—  on     disruptive     strength     of 
dielectrics,  86 

—  on  hysteresis,  no,  116 

—  on  magnetism  of  iron,  335 
Strain,  greatest,  in  belt,  193 

—  permissible  specific,  in  mate- 
rials, 189,  193 

Stranded  wire  conductors,  36,  105, 

181,  183,  376,  528,  549 
Stratton,  Alex.,  on  distribution  of 

magnetic  flux,  397 
Stray  paths  of  magnetic  flux,  218, 

300,  398 


INDEX. 


681 


Street    car    motors,    see  Railway 

Motors. 
Strength,  disruptive,  of  insulating 

materials,  83,  84,  85 

—  tensile,  of  materials,  189,  193 
Sulphur,  in  cast  steel,  288 
Surface  of  armature,  122-126 

—  of    brush-contact,    168,    174- 
176,  514 

—  of  magnet-coils,  369 
Switches,  design  of,  181-183 
Symbols  for  armature   windings, 

150 

—  used  in  formulae,  see  List  of 
Symbols. 

Symmetry  of  magnetic  field,  140, 
304 


Tables,  list  of,  see  Contents. 
Tangential   multipolar  type,  244, 
270,  281,  282 

—  pull,  see  Force. 

Tape,  for  armature-insulation,  78 

Taper-plugs,  182,  183 

Teeth  in  armature,  see  Toothed 
Core  Armatures. 

Temperature-increase  in  arma- 
ture, 126-130 

—  in  magnet-coils,  368-371 
Temperature,  influence  of,  on  hys- 
teresis, 117,   118 

—  on  insulation-resistance,  85 
Tension,  best,  for  brush-contact, 

176-179,  515 

—  safe,  in  materials,  189,  193 
Theory,  modern,   of    magnetism, 

199 

Thickness  of  armature-insulations, 
78-82 

—  of  armature-laminae,  94,  in, 
119-122 

—  of  armature-spokes,  189,  516 

—  of  belts,  194 

—  of  commutator-brushes,  174 

—  of      commutator-insulations, 
171 

Thompson,  Milton  E.,  on  magnet- 
ism of  iron,  335 

Thompson,  Professor  Silvanus  P., 
on  circumflux  of  armature,  131 

—  on  diametral  current  density 
of  armature,  133 

—  on  eddy  current-loss  in  arma- 
ture, 121 

—  on    forms    of    field-magnets,    I 
272,  273,  274,  276,  277,  278,  282,    I 
283 


Thompson,  Professor  Silvanus  P^ 
on  homopolar  and  heteropolai 
induction,  23 

—  on  leakage  formulae,  216 

—  on  prevention   of    armature- 
reaction,  465 

—  on  ratio  of  magnet-,  to  arma- 
ture-cross-section, 292,  293 

—  on  test  of  Westinghouse  No. 
3  railway  motor,  435 

Thomson,  Professor  Elihu,  on 
prevention  of  armature-reac- 
tion, 469 

Thomson,  Sir  William  (Lord  Kel- 
vin), on  efficiency  of  shunt 
dynamo,  39 

Thrusting  force,  acting  on  arma- 
ture, 140-142,  513,  534 

Timmermann,  A.  H.  and  C.  E., 
on  armature-radiation,  126 

Tool-steel,  hysteretic  resistance 
of,  in 

Toothed  core  armatures,  advan- 
tages and  disadvantages  of, 
61,  62,  63 

—  core-leakage  in,  53,  218,  219 

—  definition  of,  4 

—  dimensioning  of,  65-72 

—  effective  field-area  of,  207 

—  factor  of  field- deflection  for, 
230,  231 

—  gap-permeance  of,  227-231 

—  height  of  winding-space  in,  75 

—  hysteresis  heat  in,  67,  68,  69, 

59i 

—  insulation  of,  81 

—  number  of  slots  for,  66 

—  percentage    of  effective   gap 
circumference  for,  135 

—  percentage  of  polar  arc  for,  50 

—  seat  of  electro-dynamic  force 
in,  63,  64 

—  various  types  of  slots  for,  66 
Torque,  calculation   of,    137,  138, 

513,  534 

—  of  toothed  and  perforated  ar- 
matures, 63 

Traction-resistance,  440 

Transformation-ratio,  in  motor- 
generators,  454,  656 

Transformer,  rotary,  see  Motor- 
Generator. 

Transmission  of  power,  at  con- 
stant speed,  497 

Trapezoidal  armature -bars,  78, 
101,  567 

Triplex,  or  triple,  armature-wind- 
ing, 149,  150,  151,  156, 162, 163, 
166,  167 


682 


INDEX. 


Triply  re-entrant  armature-wind- 
ing, 150,  156,  162,  163,  164, 
167 

Troughs,  micanite,  for  insulating 
armature-slots,  81,  82 

Tubes,  insulating,  for  armature 
slots,  80,  82 

Tunnel  Armature,  see  Perforated 
Armature. 

Turn,  mean,  length  of,  on  mag- 
nets, 374 

Turning  moment,  see  Torque. 

Two-circuit  winding,  see  Series 
Armature-Winding. 

Two-coil  armature,  15,  16,  20 

Type,  selection  of,  285,  437 

Types  of  armature-winding,  153- 
157 

—  of  field-magnets,  269-285 

—  of  polepieces,  296 

—  of  series- windings,  157,  158 

—  of  slots  for  iron -clad  arma- 
tures, 66 


U 


Under-type,  270,  278,  287 
Unipolar  dynamos,  calculation  of, 
443-451,  652 

—  principle  of,  23-26 
Unipolar  induction,  22,  23 
Unit  armature-induction,  47-50 
Units,  electric,  7,  47 

—  electro-magnetic,  200,  332,  333 

—  magnetic,  199,  200 
Unsymmetrical  magnetic  field,  ef- 
fect of,  on  armature,  140-142, 
513,  534 

Unwound  poles,.  470 
Upright  horseshoe  type,  239,  245, 
249,  263,  269,  270,  527,  547,  621 
Useful  magnetic  flux,  92,  133,  200- 

202,  2II-2I4 

Utilization  of  copper,  specific,  see 
Efficiency  of  Magnetic  Field. 


Variable  resistance,  see  Rheostat. 

—  shunt  method  of  regulation, 
459 

Varnish,  for  armature-insulation, 

85,  94 
Varying  cross-section  in  magnetic 

circuit,  345,  346,  348 
Velocity  of  armature-conductors, 

6,  7,  52,  448 

—  of  belt,  193 

—  of  commutator,  179,  180,  515 


Velocity  of  railway-cars,  433,  440- 
442,  500-502 

—  of  unipolar  armatures,  448 
Ventilation  of  armature,    53,   94, 

528,  590 
Vertical  magnet  types,   252,  253, 

263,  269,  270,  273,  274,  276,  278, 

284,  285,  299   304 
Vibration    of    dynamo,    287,    300, 

43i 

"  Victoria"  dynamo,  282 

"  Volume  "   of  armature  current, 

131 

Voltage,  see  Electromotive  Force. 
Vulcabeston,  80,  84,  85 
Vulcanized  fibre,  79,  84,  85 

W 

Warburg,  on  hysteresis,  no 

Warner,  G.  M.,  on  unipolar  dy- 
namos, 25 

Wave  winding,  or  zigzag  winding, 
144,  146,  147,  153,  154 

Weaver,  W.  D.,  on  shunt  motors, 
428 

Weber,  the  unit  of  magnetic  flux, 
199,  200 

Webster,  A.  G.,  on  unipolar  dy- 
namos, 25 

Wedding,  W.,  on  magnetic  leak- 
age, 262 

Wedge-shaped  armature-conduct- 
ors, 78,  101,  567 

Weight-efficiency  of  dynamos,  33, 
410-412 

Weight  of  armature  winding,  101, 
102 

—  of  insulation  on  round  copper 
wire,  103 

—  of  magnet  winding,  366-368, 
388-390 

—  of  parts  of  dynamos,  527,  546, 
565,  579,  602 

Width,  see  Breadth. 
Wiener,  Alfred  E.,  on  calculation 
of  electric  motors,  419 

—  on   commutator-brushes,    171 

—  on    dynamo-calculation,     see 
Preface. 

—  on  efficiency  of  dynamo-elec- 
tric machinery,  405 

—  on  magnetic  leakage,  216 

—  on  ratio  of  output  and  size  of 
dynamos,  416 

Wilson,  Ernest,  on  heating  of 
drum  armatures,  130 

Winding  of  armatures,  see  Arma- 
ture-Winding. 


INDEX, 


683 


Winding  of  magnets,  see  Magnet- 
Winding. 

Winding-space,   height  of,  in   ar- 
matures, 70,  71,  74,  75 
—  height  of,  in   magnets,    317, 
36i,  371,  375,377.  386,  387 

Wire,  copper,  101,  104,  119 

—  for  armature-binding,  75 

—  gauges,  103,  367 

—  iron,  for  armature  and  mag- 
net winding,  472,  475 

—  iron,  for  armature-cores,  93, 
94,  no,  113,  115 

Wolcott,  Townsend,  on  seat  of 
electro-dynamic  force  in  iron- 
clad armatures,  64 

Wood,  for  armature-insulation,  85 

—  for  dynamo-base,  300 
Wood,  Harrison  H.,  on  curves  for 

winding  magnets,  365 
Work  done  by  armature,  137 
Working-stress,  safe,  of  different 

metals,  189 


Working-stress,   safe,  of  leather, 

193 

Worm  gearing,  434,  435 
Wrought  iron,  for  armature-cores, 

90-94,  109-122 

—  for  armature-shafts,  186 

—  for  magnet  cores,  288 

—  for  polepieces,  293 

—  for  unipolar  armatures,  448 

•  — magnetic  properties  of,    in, 

3",  313 

—  safe  working  load  of,  189 


Yokes,  dimensioning  of,  325 
—  length  of  magnetic  circuit  in, 
347 


Zigzag  winding,  see  Wave- Wind- 
ing, 
Zinc  blocks,  300-303 


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Bell,  Dr.  Louis.    Electrical  Transmission  of  Power 2.50 

Cox,  Frank  P.,  B.S.    Continuous- Current  Dynamos  and  Motors 2.00 

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Steinmetz,  C.  P.    Theory  and  Calculation  of  Alternating-Current  Phenomena.  2.5O 
Tesla,  Nikola.    Experiments  with  Alternating  Currents  of  High  Potential  and 

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Thompson,  Prof.  Silvanus  P.    Lectures  on  the  Electromagnet l.OO 

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